Condensed Consolidated Statements of Income - USD ($) shares in Millions, $ in Millions	3 Months Ended		6 Months Ended
	Apr. 03, 2022	Apr. 04, 2021	Apr. 03, 2022	Apr. 04, 2021
Income Statement [Abstract]
Net Sales	$ 807.8	$ 760.3	$ 1,565.0	$ 1,496.5
Cost of goods sold	551.0	498.0	1,088.6	981.3
Restructuring and related charges	1.2	1.3	1.5	1.4
Gross profit	255.6	261.0	474.9	513.8
Selling	144.1	121.9	280.1	236.6
General and administrative	76.0	74.8	143.6	152.5
Research and development	8.2	7.8	15.8	14.4
Restructuring and related charges	15.2	3.0	32.3	11.9
Transaction related charges	20.2	8.2	35.1	27.2
Total operating expenses	263.7	215.7	506.9	442.6
Operating (loss) income	(8.1)	45.3	(32.0)	71.2
Interest expense	24.7	52.8	46.4	76.0
Other non-operating income, net	(0.9)	(2.2)	(0.3)	(11.1)
(Loss) income from continuing operations before income taxes	(31.9)	(5.3)	(78.1)	6.3
Income tax benefit	(6.8)	(0.7)	(22.8)	(4.8)
Net (loss) income from continuing operations	(25.1)	(4.6)	(55.3)	11.1
Income from discontinued operations, net of tax	41.1	40.3	79.9	97.5
Net income	16.0	35.7	24.6	108.6
Net (loss) income from continuing operations attributable to non-controlling interest	0.0	(0.9)	0.0	0.1
Net income (loss) from discontinued operations attributable to non-controlling interest	0.1	0.0	0.5	(0.2)
Net income attributable to controlling interest	15.9	36.6	24.1	108.7
Amounts attributable to controlling interest
Net (loss) income from continuing operations attributable to controlling interest	(25.1)	(3.7)	(55.3)	11.0
Net income from discontinued operations attributable to controlling interest	41.0	40.3	79.4	97.7
Net income attributable to controlling interest	$ 15.9	$ 36.6	$ 24.1	$ 108.7
Earnings Per Share
Basic earnings per share from continuing operations (in dollars per share)	$ (0.61)	$ (0.09)	$ (1.35)	$ 0.26
Basic earnings per share from discontinued operations (in dollars per share)	1.00	0.95	1.94	2.28
Basic earnings per share (in dollars per share)	0.39	0.86	0.59	2.54
Diluted earnings per share from continuing operations (in dollars per share)	(0.61)	(0.09)	(1.35)	0.26
Diluted earnings per share from discontinued operations (in dollars per share)	1.00	0.95	1.94	2.27
Diluted earnings per share (in dollars per share)	0.39	0.86	0.59	2.53
Dividend per share (in dollars per share)	$ 0.42	$ 0.42	$ 0.84	$ 0.84
Weighted Average Shares Outstanding
Basic (in shares)	40.8	42.6	41.1	42.8
Diluted (in shares)	40.8	42.6	41.1	43.0