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Consolidated Statements of Shareholder's Equity - USD ($) shares in Millions, $ in Millions | Total | Accelerated share repurchase | Treasury stock repurchases | Total Shareholders’ Equity | Total Shareholders’ Equity Accelerated share repurchase | Total Shareholders’ Equity Treasury stock repurchases | Common Stock | Common Stock Accelerated share repurchase | Common Stock Treasury stock repurchases | Additional Paid-in Capital | Additional Paid-in Capital Accelerated share repurchase | Accumulated Earnings | Accumulated Other Comprehensive Loss | Treasury Stock | Treasury Stock Accelerated share repurchase | Treasury Stock Treasury stock repurchases | Non- controlling Interest
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Balance at beginning of period at Sep. 30, 2021 |  |  |  |  |  |  |  |  |  |  |  |  | $ (235.3) |  |  |  |
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net (loss) income from continuing operations | $ (77.0) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Income from discontinued operations, net of tax | 149.7 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Other comprehensive income, net of tax | $ (68.7) |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Treasury stock repurchases (in shares) | (1.4) | 0.0 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Treasury stock repurchases |  |  |  |  |  |  |  |  |  |  |  |  |  | $ (134.0) | $ 0.0 |  |
Balance at end of period (in shares) at Sep. 30, 2022 |  |  |  |  |  |  | 40.8 |  |  |  |  |  |  |  |  |  |
Balance at end of period at Sep. 30, 2022 | $ 1,269.1 |  |  | $ 1,263.2 |  |  | $ 0.5 |  |  | $ 2,032.5 |  | $ 362.1 | (303.1) | (828.8) |  |  | $ 5.9
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net (loss) income from continuing operations | (233.7) |  |  | (233.8) |  |  |  |  |  |  |  | (233.8) |  |  |  |  | 0.1
Income from discontinued operations, net of tax | 2,035.6 |  |  | 2,035.3 |  |  |  |  |  |  |  | 2,035.3 |  |  |  |  | 0.3
Sale and deconsolidation of assets held for sale | 19.4 |  |  | 25.3 |  |  |  |  |  |  |  |  | 25.3 |  |  |  | (5.9)
Other comprehensive income, net of tax | 28.7 |  |  | 28.4 |  |  |  |  |  |  |  |  | 28.4 |  |  |  | 0.3
Other comprehensive income, net of tax | $ 54.8 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Treasury stock repurchases (in shares) | (5.7) | (5.3) |  |  |  |  |  | (5.3) | (0.4) |  |  |  |  |  |  |  |
Treasury stock repurchases |  | $ (500.0) | $ (34.7) |  | $ (500.0) | $ (34.7) |  |  |  |  | $ (100.0) |  |  | (434.7) | (400.0) | $ (34.7) |
Excise tax on net share repurchases | $ (4.2) |  |  | (4.2) |  |  |  |  |  |  |  |  |  | (4.2) |  |  |
Restricted stock issued and related tax withholdings (in shares) |  |  |  |  |  |  | 0.2 |  |  |  |  |  |  |  |  |  |
Restricted stock issued and related tax withholdings | (12.9) |  |  | (12.9) |  |  |  |  |  | (30.3) |  |  |  | 17.4 |  |  |
Share based compensation | 18.6 |  |  | 18.6 |  |  |  |  |  | 18.6 |  |  |  |  |  |  |
Dividends declared to common shareholders | (67.6) |  |  | (67.6) |  |  |  |  |  |  |  | (67.6) |  |  |  |  |
Balance at end of period (in shares) at Sep. 30, 2023 |  |  |  |  |  |  | 35.3 |  |  |  |  |  |  |  |  |  |
Balance at end of period at Sep. 30, 2023 | 2,518.3 |  |  | 2,517.6 |  |  | $ 0.5 |  |  | 1,920.8 |  | 2,096.0 | (249.4) | (1,250.3) |  |  | 0.7
Increase (Decrease) in Stockholders' Equity [Roll Forward] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net (loss) income from continuing operations | 99.3 |  |  | 99.3 |  |  |  |  |  |  |  | 99.3 |  |  |  |  |
Income from discontinued operations, net of tax | 25.5 |  |  | 25.5 |  |  |  |  |  |  |  | 25.5 |  |  |  |  |
Other comprehensive income, net of tax | 45.5 |  |  | 45.4 |  |  |  |  |  |  |  |  | 45.4 |  |  |  | 0.1
Premium on capped call transactions, net of tax | $ (18.8) |  |  | (18.8) |  |  |  |  |  | (18.8) |  |  |  |  |  |  |
Treasury stock repurchases (in shares) | (7.4) | (1.3) |  |  |  |  |  | (1.3) | (6.1) |  |  |  |  |  |  |  |
Treasury stock repurchases |  | $ 0.0 | $ (482.7) |  | $ 0.0 | $ (482.7) |  |  |  |  | $ 83.2 |  |  | (565.9) | $ (83.2) | $ (482.7) |
Excise tax on net share repurchases | $ (5.6) |  |  | (5.6) |  |  |  |  |  |  |  |  |  | (5.6) |  |  |
Restricted stock issued and related tax withholdings (in shares) |  |  |  |  |  |  | 0.1 |  |  |  |  |  |  |  |  |  |
Restricted stock issued and related tax withholdings | (5.5) |  |  | (5.5) |  |  |  |  |  | (14.6) |  |  |  | 9.1 |  |  |
Share based compensation | 17.5 |  |  | 17.5 |  |  |  |  |  | 17.5 |  |  |  |  |  |  |
Dividends declared to common shareholders | (51.8) |  |  | (51.8) |  |  |  |  |  |  |  | (51.8) |  |  |  |  |
Balance at end of period (in shares) at Sep. 30, 2024 |  |  |  |  |  |  | 28.0 |  |  |  |  |  |  |  |  |  |
Balance at end of period at Sep. 30, 2024 | $ 2,141.7 |  |  | $ 2,140.9 |  |  | $ 0.5 |  |  | $ 1,988.1 |  | $ 2,169.0 | $ (204.0) | $ (1,812.7) |  |  | $ 0.8

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