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Equity-Based Compensation - Additional Information (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Nov. 19, 2020
Nov. 14, 2020
Nov. 14, 2019
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Mar. 10, 2020
Oct. 22, 2018
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]                
Number of stock options forfeited       355,000        
Stock option vested and exercisable upon issuance       3,432,000        
Stock options granted       687,000        
Granted, weighted average exercise price       $ 13.78        
Number of shares exercised       26,000        
Equity-based compensation       $ 19.7 $ 23.6 $ 15.7    
Unrecognized compensation cost       $ 25.6 $ 36.2 $ 40.2    
Unrecognized compensation cost, weighted average recognition period       1 year 2 months 12 days        
Restricted Stock Units                
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]                
Vesting period       4 years        
Units granted       876,000        
Units redemption       221,000        
Units forfeited or canceled       105,000        
Units outstanding       1,299,000 749,000      
Share issued to holders of units       876,000        
Stock options weighted average grant date fair value       $ 14.28        
Non-cash equity-based compensation expense over the requisite service period       $ 10.5        
Granted, weighted average exercise price       $ 14.28        
Number of shares exercised       221,000        
Common stock shares issued       876,000        
Restricted Stock Awards                
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]                
Units granted              
Units redemption       253,000        
Units forfeited or canceled       68,000        
Units outstanding       802,000 1,123,000      
Granted, weighted average exercise price              
Stock Options                
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]                
Vesting period 4 years              
Share issued to holders of units 687,000              
Stock options weighted average grant date fair value $ 6.71              
Weighted average exercise price $ 13.78              
Non-cash equity-based compensation expense over the requisite service period $ 4.1              
Number of shares forfeited       355,000        
Number of shares exercised       26,000        
Common stock shares issued 687,000              
Amended and Restated 2018 Omnibus Incentive Plan                
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]                
Number of shares of common stock that may be issued             18,650,000  
ESPP                
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]                
Share issued to holders of units   120,000 172,000          
Common stock shares available for sale               1,100,000
Common stock shares issued   120,000 172,000