Goodwill and Intangible Assets - Schedule of Intangible Assets and Goodwill (Details) - USD ($) $ in Millions	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Indefinite-lived intangible assets:
Net goodwill	$ 80.7	$ 93.7	$ 98.6
Intangible Assets, Gross, (Including Goodwill)	762.6	763.7
Accumulated amortization:
Accumulated Amortization	460.6	438.1
Intangible assets, net	309.7	334.0
Business combination-related intangible assets, net
Accumulated amortization:
Net book value	302.0	325.6
Trade names and trademarks
Indefinite-lived intangible assets:
Trade names and trademarks	272.5	272.6
Capitalized internal-use software:
Capitalized external-use software:
Capitalized Computer Software, Gross	40.1	38.1
Accumulated amortization	32.4	29.7
Net book value	7.7	8.4
Technology
Finite-lived intangible assets:
Technology	118.6	119.6
Accumulated amortization:
Accumulated Amortization	97.9	95.3
Customer relationships and other
Finite-lived intangible assets:
Customer relationships and other	371.5	371.5
Accumulated amortization:
Accumulated Amortization	$ 362.7	$ 342.8