Condensed Consolidated Statements of Income - USD ($) shares in Millions, $ in Millions	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Apr. 02, 2023	Mar. 31, 2024	Apr. 02, 2023
Income Statement [Abstract]
Net sales	$ 718.5	$ 729.2	$ 1,410.7	$ 1,442.5
Cost of goods sold	445.1	514.7	892.3	1,026.1
Gross profit	273.4	214.5	518.4	416.4
Selling, general & administrative	223.5	224.5	439.4	448.1
Impairment of intangible assets	39.0	67.0	43.0	67.0
Representation and warranty insurance proceeds	(65.0)	0.0	(65.0)	0.0
Gain from remeasurement of contingent consideration liability	0.0	0.0	0.0	(1.5)
Total operating expenses	197.5	291.5	417.4	513.6
Operating income (loss)	75.9	(77.0)	101.0	(97.2)
Interest expense	16.9	31.6	36.1	65.0
Interest income	(17.5)	(0.2)	(40.9)	(0.4)
Gain from debt repurchase	0.0	0.0	(4.7)	0.0
Other non-operating expense, net	1.1	1.4	5.2	0.1
Income (loss) from continuing operations before income taxes	75.4	(109.8)	105.3	(161.9)
Income tax expense (benefit)	25.5	(34.8)	37.9	(46.9)
Net income (loss) from continuing operations	49.9	(75.0)	67.4	(115.0)
Income from discontinued operations, net of tax	11.0	21.4	22.7	40.9
Net income (loss)	60.9	(53.6)	90.1	(74.1)
Net (loss) income from continuing operations attributable to non-controlling interest	(0.2)	0.1	(0.1)	0.3
Income from discontinued operations attributable to non-controlling interest, net of tax	0.0	0.0	0.0	0.2
Net income (loss) attributable to controlling interest	61.1	(53.7)	90.2	(74.6)
Amounts attributable to controlling interest
Net income (loss) from continuing operations attributable to controlling interest	50.1	(75.1)	67.5	(115.3)
Income from discontinued operations attributable to controlling interest, net of tax	11.0	21.4	22.7	40.7
Net income (loss) attributable to controlling interest	$ 61.1	$ (53.7)	$ 90.2	$ (74.6)
Earnings Per Share
Basic earnings per share from continuing operations (in dollars per share)	$ 1.66	$ (1.83)	$ 2.10	$ (2.82)
Basic earnings per share from discontinued operations (in dollars per share)	0.37	0.52	0.71	1.00
Basic earnings per share (in dollars per share)	2.03	(1.31)	2.81	(1.82)
Diluted earnings per share from continuing operations (in dollars per share)	1.65	(1.83)	2.09	(2.82)
Diluted earnings per share from discontinued operations (in dollars per share)	0.36	0.52	0.71	1.00
Diluted earnings per share (in dollars per share)	2.01	(1.31)	2.80	(1.82)
Dividend per share (in dollars per share)	$ 0.42	$ 0.42	$ 0.84	$ 0.84
Weighted Average Shares Outstanding
Basic (in shares)	30.2	41.0	32.1	40.9
Diluted (in shares)	30.4	41.0	32.2	40.9