Goodwill and Purchased Intangible Assets - Schedule of Purchased Intangible Assets (Details) - USD ($) $ in Millions	3 Months Ended	12 Months Ended
	Mar. 31, 2021	Sep. 30, 2020
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	14 years 1 month 6 days	14 years 8 months 12 days
Gross	$ 763.1	$ 731.2
Accumulated Amortization	(700.6)	(697.7)
Net	62.5	33.5
Non-amortizable trade names	384.8	384.7
Intangible assets excluding goodwill, gross	1,147.9	1,115.9
Purchased intangible assets, net	$ 447.3	$ 418.2
Distribution network
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	39 years 2 months 12 days	39 years 1 month 6 days
Gross	$ 55.3	$ 55.4
Accumulated Amortization	(34.4)	(33.8)
Net	$ 20.9	$ 21.6
Technology-related
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	11 years 10 months 24 days	11 years 10 months 24 days
Gross	$ 104.8	$ 104.7
Accumulated Amortization	(103.6)	(103.3)
Net	$ 1.2	$ 1.4
Customer relationships
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	12 years 9 months 18 days	12 years 9 months 18 days
Gross	$ 554.2	$ 554.7
Accumulated Amortization	(546.6)	(545.6)
Net	$ 7.6	$ 9.1
Other
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	16 years 4 months 24 days	16 years 3 months 18 days
Gross	$ 16.5	$ 16.4
Accumulated Amortization	(15.1)	(15.0)
Net	$ 1.4	$ 1.4
Amortizable Intangible Assets Before Preliminary Acquisition
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	14 years 4 months 24 days
Gross	$ 730.8
Accumulated Amortization	(699.7)
Net	$ 31.1
Preliminary acquisition amortizable intangible assets
Acquired Finite Lived Intangible Assets [Line Items]
Weighted- Average Life (in years)	7 years
Gross	$ 32.3
Accumulated Amortization	(0.9)
Net	$ 31.4