Other Intangible Assets - Schedule of Finite-Lived Intangible Assets (Details) - USD ($) $ in Millions	12 Months Ended
	Sep. 30, 2020	Sep. 30, 2019
Finite Lived Intangible Assets [Line Items]
Weighted Avg. Life (in years)	15 years 6 months
Gross Carrying Amount	$ 5,663.7	$ 5,654.3
Accumulated Amortization	$ (1,996.5)	(1,594.8)
Customer Relationships [Member]
Finite Lived Intangible Assets [Line Items]
Weighted Avg. Life (in years)	15 years 6 months
Gross Carrying Amount	$ 5,418.1	5,395.5
Accumulated Amortization	$ (1,841.2)	(1,452.1)
Trademarks and Trade Names [Member]
Finite Lived Intangible Assets [Line Items]
Weighted Avg. Life (in years)	21 years 7 months 6 days
Gross Carrying Amount	$ 130.5	129.9
Accumulated Amortization	$ (65.7)	(55.3)
Favorable Contracts [Member]
Finite Lived Intangible Assets [Line Items]
Weighted Avg. Life (in years)	7 years 2 months 12 days
Gross Carrying Amount	$ 44.0	57.0
Accumulated Amortization	$ (41.6)	(42.6)
Technology and Patents [Member]
Finite Lived Intangible Assets [Line Items]
Weighted Avg. Life (in years)	11 years 4 months 24 days
Gross Carrying Amount	$ 37.5	39.2
Accumulated Amortization	$ (21.6)	(21.2)
Licensing Agreements [Member]
Finite Lived Intangible Assets [Line Items]
Weighted Avg. Life (in years)	8 years
Gross Carrying Amount	$ 26.5	25.7
Accumulated Amortization	$ (22.8)	(20.5)
Noncompete Agreements [Member]
Finite Lived Intangible Assets [Line Items]
Weighted Avg. Life (in years)	2 years
Gross Carrying Amount	$ 3.4	3.4
Accumulated Amortization	$ (3.3)	(2.9)
Other [Member]
Finite Lived Intangible Assets [Line Items]
Weighted Avg. Life (in years)	29 years 6 months
Gross Carrying Amount	$ 3.7	3.6
Accumulated Amortization	$ (0.3)	$ (0.2)