Condensed Consolidated Statements of Income - USD ($) shares in Millions, $ in Millions	3 Months Ended
	Jan. 02, 2022	Jan. 03, 2021
Income Statement [Abstract]
Net Sales	$ 757.2	$ 736.2
Cost of goods sold	537.6	483.3
Restructuring and related charges	0.3	0.1
Gross profit	219.3	252.8
Selling	136.0	114.8
General and administrative	67.5	77.8
Research and development	7.6	6.5
Restructuring and related charges	17.1	8.9
Transaction related charges	14.9	19.0
Total operating expenses	243.1	227.0
Operating (loss) income	(23.8)	25.8
Interest expense	21.8	23.1
Other non-operating expense (income), net	0.6	(8.9)
(Loss) income from continuing operations before income taxes	(46.2)	11.6
Income tax benefit	(16.0)	(4.1)
Net (loss) income from continuing operations	(30.2)	15.7
Income from discontinued operations, net of tax	38.8	57.2
Net income	8.6	72.9
Net income from continuing operations attributable to non-controlling interest	0.0	1.0
Net income (loss) from discontinued operations attributable to non-controlling interest	0.4	(0.2)
Net income attributable to controlling interest	8.2	72.1
Amounts attributable to controlling interest
Net (loss) income from continuing operations attributable to controlling interest	(30.2)	14.7
Net income from discontinued operations attributable to controlling interest	38.4	57.4
Net income attributable to controlling interest	$ 8.2	$ 72.1
Earnings Per Share
Basic earnings per share from continuing operations (in dollars per share)	$ (0.73)	$ 0.34
Basic earnings per share from discontinued operations (in dollars per share)	0.93	1.34
Basic earnings per share (in dollars per share)	0.20	1.68
Diluted earnings per share from continuing operations (in dollars per share)	(0.73)	0.34
Diluted earnings per share from discontinued operations (in dollars per share)	0.93	1.34
Diluted earnings per share (in dollars per share)	0.20	1.68
Dividend per share (in dollars per share)	$ 0.42	$ 0.42
Weighted Average Shares Outstanding
Basic (in shares)	41.3	42.9
Diluted (in shares)	41.3	43.0