Question
$$\frac{2x-2}{6}\frac{8x^2}{6x-6} = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 1 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2x-2}{6}\frac{8x^2}{6x-6} &= 0&& \text{multiply ALL terms by } \color{blue}{ 6(6x-6) }. \\[1 em]6(6x-6)\frac{2x-2}{6}\frac{8x^2}{6x-6} &= 6(6x-6)\cdot0&& \text{cancel out the denominators} \\[1 em]16x^3-16x^2 &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 16x^{3}-16x^{2} = 0 } $, first we need to factor our $ x^2 $.
$$ 16x^{3}-16x^{2} = x^2 \left( 16x-16 \right) $$$ x = 0 $ is a root of multiplicity $ 2 $.
The second root can be found by solving equation $ 16x-16 = 0$.
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