Intangible Assets - Schedule of Finite-Lived Intangible Assets (Details) - USD ($) $ in Millions	Sep. 30, 2024	Sep. 30, 2023
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	$ 173.5	$ 175.4
Accumulated amortization	(83.2)	(72.8)
Net carrying amount	90.3	102.6
Trademarks and trade names
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	29.2	29.6
Accumulated amortization	(11.4)	(10.5)
Net carrying amount	17.8	19.1
Reacquired franchise rights
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	122.2	122.1
Accumulated amortization	(58.7)	(49.4)
Net carrying amount	63.5	72.7
Customer relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	15.1	16.8
Accumulated amortization	(7.9)	(8.3)
Net carrying amount	7.2	8.5
Other intangible assets
Finite-Lived Intangible Assets [Line Items]
Gross carrying amount	7.0	6.9
Accumulated amortization	(5.2)	(4.6)
Net carrying amount	$ 1.8	$ 2.3