$$x+\frac{1}{2}x+5\frac{x}{2}x = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -\dfrac{ 3 }{ 5 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x+\frac{1}{2}x+5\frac{x}{2}x &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2x+2 \cdot \frac{1}{2}x+25\frac{x}{2}x &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]2x+x+5x^2 &= 0&& \text{simplify left side} \\[1 em]5x^2+3x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 5x^{2}+3x = 0 } $, first we need to factor our $ x $.
$$ 5x^{2}+3x = x \left( 5x+3 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ 5x+3 = 0$.
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