Question
$$x = 4x\cdot(30-\frac{4x}{5})$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = \dfrac{ 595 }{ 16 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x &= 4x\cdot(30-\frac{4x}{5})&& \text{simplify right side} \\[1 em]x &= 4x \cdot \frac{-4x+150}{5}&& \\[1 em]x &= \frac{-16x^2+600x}{5}&& \text{multiply ALL terms by } \color{blue}{ 5 }. \\[1 em]5x &= 5 \cdot \frac{-16x^2+600x}{5}&& \text{cancel out the denominators} \\[1 em]5x &= -16x^2+600x&& \text{move all terms to the left hand side } \\[1 em]5x+16x^2-600x &= 0&& \text{simplify left side} \\[1 em]16x^2-595x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 16x^{2}-595x = 0 } $, first we need to factor our $ x $.
$$ 16x^{2}-595x = x \left( 16x-595 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ 16x-595 = 0$.
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