Earnings Per Share (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended								12 Months Ended
	Sep. 30, 2022	Jun. 30, 2022	Mar. 31, 2022	Dec. 31, 2021	Sep. 30, 2021	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2020	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Numerator
Income from continuing operations	$ 12.4	$ 39.8	$ 23.0	$ 34.2	$ 124.7	$ 49.0	$ 8.3	$ 18.1	$ 109.4	$ 200.1	$ 69.6
Income from discontinued operations, net of tax	145.3	58.4	58.4	52.8	44.2	47.9	59.5	68.6	314.9	220.2	247.0
Net income	$ 157.7	$ 98.2	$ 81.4	$ 87.0	$ 168.9	$ 96.9	$ 67.8	$ 86.7	$ 424.3	$ 420.3	$ 316.6
Denominator
Weighted-average shares common shares outstanding (in shares)									179.1	182.5	187.0
Effect of potentially dilutive securities (in shares)									1.3	1.0	0.5
Weighted-average diluted shares outstanding (in shares)									180.4	183.5	187.5
Basic earnings per share
Discontinued operations, basic earnings per share (usd per share)	$ 0.82	$ 0.33	$ 0.32	$ 0.29	$ 0.24	$ 0.26	$ 0.32	$ 0.37	$ 1.76	$ 1.20	$ 1.32
Continuing operations, basic earnings per share (usd per share)	0.07	0.22	0.13	0.19	0.69	0.27	0.05	0.10	0.61	1.10	0.38
Basic earnings per share (usd per share)	0.89	0.55	0.45	0.48	0.93	0.53	0.37	0.47	2.37	2.30	1.70
Diluted earnings per share
Continuing operations, diluted earnings per share (usd per share)	0.07	0.22	0.13	0.19	0.68	0.27	0.05	0.10	0.61	1.09	0.37
Discontinued operations, diluted earnings per share (usd per share)	0.81	0.33	0.32	0.29	0.24	0.26	0.32	0.37	1.74	1.20	1.32
Diluted earnings per share (usd per share)	$ 0.88	$ 0.55	$ 0.45	$ 0.48	$ 0.92	$ 0.53	$ 0.37	$ 0.47	$ 2.35	$ 2.29	$ 1.69
Antidilutive securities excluded from computation of earnings per share, amount											1.0