Intangible Assets, net (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 31, 2023	Dec. 31, 2024	Sep. 30, 2024
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross		$ 328.2	$ 328.2
Finite-lived intangible assets, accumulated amortization		(190.6)	(186.4)
Finite-lived intangible assets, net		137.6	141.8
Accelerated amortization	$ 17.4
Customer relationships
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross		160.7	160.7
Finite-lived intangible assets, accumulated amortization		(96.8)	(94.6)
Finite-lived intangible assets, net		63.9	66.1
Trademarks and brands
Finite-Lived Intangible Assets
Finite-lived intangible assets, gross		164.4	164.4
Finite-lived intangible assets, accumulated amortization		(90.7)	(88.7)
Finite-lived intangible assets, net		73.7	75.7
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