Condensed Consolidated Statements of Shareholders' Equity (unaudited) Statement - USD ($)	Total	Common Stock [Member]	Additional Paid-in Capital [Member]	Retained Earnings [Member]	AOCI Attributable to Parent [Member]	Treasury Stock [Member]
Common Stock, Shares, Outstanding, Beginning Balance at Sep. 30, 2018		88,457,634
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Beginning Balance at Sep. 30, 2018	$ 1,616,200,000	$ 4,400,000	$ 602,900,000	$ 1,876,200,000	$ (113,000,000.0)	$ (754,300,000)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Cumulative Effect on Retained Earnings, Net of Tax | Accounting Standards Update 2014-09 [Member]	(4,900,000)			(4,900,000)
Cumulative Effect on Retained Earnings, Net of Tax | Accounting Standards Update 2016-16 [Member]	(5,600,000)			(5,600,000)
New Accounting Pronouncement or Change in Accounting Principle, Effect of Adoption, Quantification				5,400,000	(5,400,000)
Net Income	124,300,000
Net Income (Loss) Attributable to Parent	124,300,000
Other Comprehensive Income (Loss), Net of Tax	(26,800,000)				(26,800,000)
Dividends	(41,400,000)		300,000	(41,700,000)
Payment, Tax Withholding, Share-based Payment Arrangement	(4,200,000)					(4,200,000)
Payments for Repurchase of Common Stock	(75,000,000.0)					(75,000,000.0)
Share-based Compensation on Equity-Classified Awards	26,700,000		26,700,000
Stock Issued During Period, Value, Stock Options Exercised	(9,200,000)		(2,100,000)			(7,100,000)
APIC, Share-based Payment Arrangement, Restricted Stock Unit, Increase for Cost Recognition			(4,900,000)
Stock Issued During Period, Value, Restricted Stock Award, Gross	0					4,900,000
Stock Issued During Period, Value, Employee Stock Purchase Plan	6,200,000		3,900,000			2,300,000
Cumulative Effect on Retained Earnings, Tax | Accounting Standards Update 2014-09 [Member]				4,800,000
Cumulative Effect on Retained Earnings, Tax | Accounting Standards Update 2016-16 [Member]				200,000
Payments for Repurchase of Common Stock	$ (75,000,000.0)
Other Comprehensive Income (Loss), Tax					4,000,000.0
Common Stock, Dividends, Per Share, Cash Paid	$ 0.62
Common Stock, Shares, Outstanding, Ending Balance at Jun. 30, 2019		88,457,634
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Ending Balance at Jun. 30, 2019	$ 1,624,700,000	$ 4,400,000	631,000,000.0	1,953,700,000	(145,200,000)	(819,200,000)
Common Stock, Shares, Outstanding, Beginning Balance at Mar. 31, 2019		88,457,634
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Beginning Balance at Mar. 31, 2019	1,598,800,000	$ 4,400,000	619,900,000	1,935,200,000	(140,300,000)	(820,400,000)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net Income	32,600,000
Net Income (Loss) Attributable to Parent	32,600,000
Other Comprehensive Income (Loss), Net of Tax	(4,900,000)				(4,900,000)
Dividends	(14,000,000.0)		100,000	14,100,000
Payment, Tax Withholding, Share-based Payment Arrangement	(200,000)					200,000
Share-based Compensation on Equity-Classified Awards	9,800,000		9,800,000
Stock Issued During Period, Value, Stock Options Exercised	(600,000)		(100,000)			(500,000)
APIC, Share-based Payment Arrangement, Restricted Stock Unit, Increase for Cost Recognition			(200,000)
Stock Issued During Period, Value, Restricted Stock Award, Gross	0					200,000
Stock Issued During Period, Value, Employee Stock Purchase Plan	$ 2,000,000.0		1,300,000			700,000
Other Comprehensive Income (Loss), Tax					(2,500,000)
Common Stock, Dividends, Per Share, Cash Paid	$ 0.21
Common Stock, Shares, Outstanding, Ending Balance at Jun. 30, 2019		88,457,634
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Ending Balance at Jun. 30, 2019	$ 1,624,700,000	$ 4,400,000	631,000,000.0	1,953,700,000	(145,200,000)	(819,200,000)
Common Stock, Shares, Outstanding, Beginning Balance at Sep. 30, 2019	66,625,011	88,457,634
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Beginning Balance at Sep. 30, 2019	$ 1,573,300,000	$ 4,400,000	637,400,000	1,967,400,000	(182,500,000)	(853,400,000)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Cumulative Effect on Retained Earnings, Net of Tax | Accounting Standards Update 2014-09 [Member]	300,000			300,000
Net Income	180,600,000
Net Income (Loss) Attributable to Parent	180,600,000
Other Comprehensive Income (Loss), Net of Tax	(29,700,000)				(29,700,000)
Dividends	(43,300,000)		400,000	(43,700,000)
Payment, Tax Withholding, Share-based Payment Arrangement	(16,400,000)					16,400,000
Payments for Repurchase of Common Stock	(54,100,000)					(54,100,000)
Share-based Compensation on Equity-Classified Awards	26,400,000		26,400,000
Stock Issued During Period, Value, Stock Options Exercised	(8,500,000)		(2,900,000)			(5,600,000)
APIC, Share-based Payment Arrangement, Restricted Stock Unit, Increase for Cost Recognition			(16,900,000)
Stock Issued During Period, Value, Restricted Stock Award, Gross	0					16,900,000
Stock Issued During Period, Value, Employee Stock Purchase Plan	6,800,000		4,200,000			2,600,000
Stock Issued During Period, Shares, Employee Stock Purchase Plans		0
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Vested in Period		0
Cumulative Effect on Retained Earnings, Tax | Accounting Standards Update 2014-09 [Member]				100,000
Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercises in Period		0
Payments for Repurchase of Common Stock	$ 54,100,000
Other Comprehensive Income (Loss), Tax					11,400,000
Common Stock, Dividends, Per Share, Cash Paid	$ 0.65
Common Stock, Shares, Outstanding, Ending Balance at Jun. 30, 2020	66,602,366	88,457,634
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Ending Balance at Jun. 30, 2020	$ 1,652,400,000	$ 4,400,000	654,400,000	2,104,600,000	(212,200,000)	(898,800,000)
Common Stock, Shares, Outstanding, Beginning Balance at Mar. 31, 2020		88,457,634
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Beginning Balance at Mar. 31, 2020	1,548,900,000	$ 4,400,000	644,400,000	2,025,200,000	(223,600,000)	(901,500,000)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Cumulative Effect on Retained Earnings, Net of Tax | Accounting Standards Update 2014-09 [Member]	300,000			300,000
Net Income	93,900,000
Net Income (Loss) Attributable to Parent	93,900,000
Other Comprehensive Income (Loss), Net of Tax	11,400,000				11,400,000
Dividends	14,600,000		200,000	14,800,000
Payment, Tax Withholding, Share-based Payment Arrangement	600,000					600,000
Share-based Compensation on Equity-Classified Awards	7,900,000		7,900,000
Stock Issued During Period, Value, Stock Options Exercised	(2,800,000)		(1,200,000)			(1,600,000)
APIC, Share-based Payment Arrangement, Restricted Stock Unit, Increase for Cost Recognition			(800,000)
Stock Issued During Period, Value, Restricted Stock Award, Gross	(100,000)					700,000
Stock Issued During Period, Value, Employee Stock Purchase Plan	$ 2,500,000		1,500,000			1,000,000.0
Cumulative Effect on Retained Earnings, Tax | Accounting Standards Update 2014-09 [Member]				100,000
Other Comprehensive Income (Loss), Tax					(1,600,000)
Common Stock, Dividends, Per Share, Cash Paid	$ 0.22
Common Stock, Shares, Outstanding, Ending Balance at Jun. 30, 2020	66,602,366	88,457,634
Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Ending Balance at Jun. 30, 2020	$ 1,652,400,000	$ 4,400,000	$ 654,400,000	$ 2,104,600,000	$ (212,200,000)	$ (898,800,000)