Solve:
$m - 1 - {(m - 1)}^{2} + a m - a$

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Solution

$(m - 1) - (m - 1)^{2} + a m - a = 0$

$\Rightarrow (m - 1) - (m - 1)^{2} + a (m - 1) = 0$

$\Rightarrow (m - 1) {1 - (m - 1) + a} = 0$

$\Rightarrow (m - 1) {- m + 2 + a} = 0$

$\Rightarrow m - 1 = 0$ or $a + 2 - m = 0$

$\Rightarrow m = 1$ or $m = 2 + a$

$∴ m = 1$ or $m = 2 + a$

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