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Stockholders' Equity and Weighted Average Common Shares Outstanding - Additional Information (Details) - USD ($)
12 Months Ended
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2018
May 31, 2020
Oct. 31, 2018
Nov. 30, 2016
Equity, Class of Treasury Stock [Line Items]            
Common stock, authorized (shares) 600,000,000 600,000,000        
Common stock, par value (usd per share) $ 0.01 $ 0.01        
Preferred stock, authorized (shares) 10,000,000          
Preferred stock, par value (usd per share) $ 0.01          
Preferred stock, issued (shares) 0          
Shares repurchased $ 405,692,000 $ 664,803,000 $ 663,220,000      
Antidilutive securities excluded from computation of diluted earnings per share (shares) 4,200,000 4,600,000 3,200,000      
November 2016 Share Repurchase Program            
Equity, Class of Treasury Stock [Line Items]            
Share repurchase program, authorized amount           $ 1,000,000,000.0
Shares repurchased (shares)   1,400,000 7,700,000      
Shares repurchased   $ 125,800,000 $ 663,100,000      
Shares repurchased, cash settled     $ 24,000,000.0      
October 2018 Share Repurchase Program            
Equity, Class of Treasury Stock [Line Items]            
Share repurchase program, authorized amount         $ 1,000,000,000.0  
Shares repurchased (shares) 4,900,000 6,700,000        
Shares repurchased $ 405,600,000 $ 538,900,000        
Shares repurchased, cash settled   $ 14,800,000        
Share repurchase program, availability remaining $ 55,500,000          
May 2020 Share Repurchase Program            
Equity, Class of Treasury Stock [Line Items]            
Share repurchase program, authorized amount       $ 500,000,000