Stockholders' Equity (Common Stock Outstanding) (Details) - USD ($)	3 Months Ended
	Nov. 30, 2019	Nov. 30, 2018	Sep. 30, 2019
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Common stock outstanding, beginning balances (in shares)	153,520,380
Common stock outstanding, ending balance (in shares)	152,300,356
2020 Share Repurchase Program
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Share repurchase program, amount authorized			$ 600,000,000.0
Number of shares repurchased	2,600,000
Value of shares repurchased	$ 96,400,000
Share repurchase program, remaining amount available	$ 503,600,000
Common Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Common stock outstanding, beginning balances (in shares)	153,520,380	164,588,172
Shares issued upon exercise of stock options (in shares)	13,930	0
Shares issued under employee stock purchase plan (in shares)	0	354
Vesting of restricted stock (in shares)	1,916,740	1,686,163
Purchases of treasury stock under employee stock plans (in shares)	(530,417)	(407,447)
Treasury shares purchased (in shares)	(2,620,277)	(7,880,346)
Common stock outstanding, ending balance (in shares)	152,300,356	157,986,896