Debt - Schedule of Debt (Details) - Madison Industries IAQ Solutions Corporation - USD ($) $ in Millions	Mar. 31, 2026	Dec. 31, 2025
Debt Instrument [Line Items]
Equipment loans and financing leases	$ 6.2	$ 5.7
Discounts and financing fees, net	(63.8)	(68.6)
Total debt	5,648.7	5,650.4
Long-term debt, net of current maturities	(27.7)	(27.8)
Less: Current maturities	5,621.0	5,622.6
Senior notes
Debt Instrument [Line Items]
Long-term debt, gross	1,035.0	1,035.0
Senior secured notes
Debt Instrument [Line Items]
Long-term debt, gross	700.0	700.0
Mortgage payable
Debt Instrument [Line Items]
Long-term debt, gross	0.0	0.6
Credit Agreement | Line of Credit
Debt Instrument [Line Items]
Long-term debt, gross	$ 3,971.3	$ 3,977.7