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Intangible Assets - Schedule of Finite-Lived Intangible Assets (Details) - USD ($)
$ in Millions
Mar. 31, 2026
Sep. 30, 2025
Finite-Lived Intangible Assets [Line Items]    
Gross carrying amount $ 196.9 $ 173.9
Accumulated amortization (99.1) (91.4)
Net carrying amount 97.8 82.5
Trademarks and trade names    
Finite-Lived Intangible Assets [Line Items]    
Gross carrying amount 37.5 29.5
Accumulated amortization (14.4) (12.7)
Net carrying amount 23.1 16.8
Reacquired franchise rights    
Finite-Lived Intangible Assets [Line Items]    
Gross carrying amount 126.1 122.3
Accumulated amortization (69.0) (63.9)
Net carrying amount 57.1 58.4
Customer relationships    
Finite-Lived Intangible Assets [Line Items]    
Gross carrying amount 25.7 14.7
Accumulated amortization (9.2) (8.5)
Net carrying amount 16.5 6.2
Other intangible assets    
Finite-Lived Intangible Assets [Line Items]    
Gross carrying amount 7.6 7.4
Accumulated amortization (6.5) (6.3)
Net carrying amount $ 1.1 $ 1.1