Question
$$\frac{1}{2}(4x+2)(2x-2) = 0$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = -\dfrac{ 1 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{2}(4x+2)(2x-2) &= 0&& \text{simplify left side} \\[1 em]\frac{4x+2}{2}(2x-2) &= 0&& \\[1 em]\frac{8x^2-4x-4}{2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{8x^2-4x-4}{2} &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]8x^2-4x-4 &= 0&& \\[1 em] \end{aligned} $$
$ 8x^{2}-4x-4 = 0 $ is a quadratic equation.
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