$$\frac{1}{10}x-\frac{2x}{4+4x^2} = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 2 & x_3 = -2 \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{10}x-\frac{2x}{4+4x^2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 10\cdot(4+4x^2) }. \\[1 em]10\cdot(4+4x^2)\frac{1}{10}x-10\cdot(4+4x^2)\frac{2x}{4+4x^2} &= 10\cdot(4+4x^2)\cdot0&& \text{cancel out the denominators} \\[1 em]4x^3+4x-20x &= 0&& \text{simplify left side} \\[1 em]4x^3-16x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 4x^{3}-16x = 0 } $, first we need to factor our $ x $.
$$ 4x^{3}-16x = x \left( 4x^{2}-16 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 4x^{2}-16 = 0$.
$ 4x^{2}-16 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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