Question
$$(x-1)^2+8(x-1) = -15$$
Answer
$$ \begin{matrix}x_1 = -2 & x_2 = -4 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (x-1)^2+8(x-1) &= -15&& \text{simplify left side} \\[1 em]x^2-2x+1+8(x-1) &= -15&& \\[1 em]x^2-2x+1+8x-8 &= -15&& \\[1 em]x^2+6x-7 &= -15&& \text{move all terms to the left hand side } \\[1 em]x^2+6x-7+15 &= 0&& \text{simplify left side} \\[1 em]x^2+6x+8 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+6x+8 = 0 $ is a quadratic equation.
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