Question
$$x \cdot \frac{x-8}{x}-8 = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 16 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x \cdot \frac{x-8}{x}-8 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]xx \cdot \frac{x-8}{x}-x\cdot8 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]x^2-8x-8x &= 0&& \text{simplify left side} \\[1 em]x^2-16x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ x^{2}-16x = 0 } $, first we need to factor our $ x $.
$$ x^{2}-16x = x \left( x-16 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ x-16 = 0$.
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