Debt - Term loan (Details) - USD ($) $ in Thousands	1 Months Ended	12 Months Ended
	Jul. 31, 2017	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Debt Instruments
Remaining aggregate outstanding principal amount paid		$ 770,286	$ 422,258	$ 882,921
Loss on extinguishment of debt from write-off of unamortized deferred financing costs		$ (16,439)	(4,260)	$ (38)
Term loan B
Debt Instruments
Remaining aggregate outstanding principal amount paid			1,400
Fixed Rate Tranche | Term loan B
Debt Instruments
Remaining aggregate outstanding principal amount paid			213,200
Loss on extinguishment of debt from write-off of unamortized deferred financing costs			(1,400)
Variable-rate tranche | Term loan B
Debt Instruments
Remaining aggregate outstanding principal amount paid			8,300
Loss on extinguishment of debt from write-off of unamortized deferred financing costs			$ (100)
Sally Holdings, LLC | Term Loan B
Debt Instruments
Debt instrument term	7 years
Debt instrument, face amount	$ 850,000
Debt instrument, maturity date	Jul. 05, 2024