Question
$$2(x-4)\cdot\frac{1}{2}\cdot(5-3x) = 0$$
Answer
$$ \begin{matrix}x_1 = 4 & x_2 = \dfrac{ 5 }{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2(x-4)\cdot\frac{1}{2}\cdot(5-3x) &= 0&& \text{simplify left side} \\[1 em](2x-8)\cdot\frac{1}{2}\cdot(5-3x) &= 0&& \\[1 em]\frac{2x-8}{2}\cdot(5-3x) &= 0&& \\[1 em]\frac{-6x^2+34x-40}{2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{-6x^2+34x-40}{2} &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]-6x^2+34x-40 &= 0&& \\[1 em] \end{aligned} $$
$ -6x^{2}+34x-40 = 0 $ is a quadratic equation.
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