Intangible Assets, net (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2023	Sep. 30, 2023
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross	$ 375.5	$ 375.5
Finite-lived intangible assets, accumulated amortization	(220.9)	(198.7)
Finite-lived intangible assets, net	154.6	176.8
Accelerated amortization	17.4
Customer relationships
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross	178.4	178.4
Finite-lived intangible assets, accumulated amortization	(105.8)	(97.2)
Finite-lived intangible assets, net	72.6	81.2
Trademarks and brands
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross	194.0	194.0
Finite-lived intangible assets, accumulated amortization	(112.0)	(98.4)
Finite-lived intangible assets, net	82.0	95.6
Other intangible assets
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross	3.1	3.1
Finite-lived intangible assets, accumulated amortization	(3.1)	(3.1)
Finite-lived intangible assets, net	$ 0.0	$ 0.0