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