Question
$$90 \cdot \frac{x}{x+6} = x$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 84 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 90 \cdot \frac{x}{x+6} &= x&& \text{multiply ALL terms by } \color{blue}{ x+6 }. \\[1 em](x+6)\cdot90 \cdot \frac{x}{x+6} &= (x+6)x&& \text{cancel out the denominators} \\[1 em]90x &= x^2+6x&& \text{move all terms to the left hand side } \\[1 em]90x-x^2-6x &= 0&& \text{simplify left side} \\[1 em]-x^2+84x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -x^{2}+84x = 0 } $, first we need to factor our $ x $.
$$ -x^{2}+84x = x \left( -x+84 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ -x+84 = 0$.
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