Question
$$12x-6 \cdot \frac{x}{2}x = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 4 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 12x-6 \cdot \frac{x}{2}x &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot12x-26 \cdot \frac{x}{2}x &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]24x-6x^2 &= 0&& \text{simplify left side} \\[1 em]-6x^2+24x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -6x^{2}+24x = 0 } $, first we need to factor our $ x $.
$$ -6x^{2}+24x = x \left( -6x+24 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ -6x+24 = 0$.
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