$$x\cdot(1-x^2) = -x$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -\sqrt{ 2 } & x_3 = \sqrt{ 2 } \end{matrix} $$
Explanation
$$ \begin{aligned} x\cdot(1-x^2) &= -x&& \text{simplify left side} \\[1 em]x-x^3 &= -x&& \\[1 em]-x^3+x &= -x&& \text{move all terms to the left hand side } \\[1 em]-x^3+x+x &= 0&& \text{simplify left side} \\[1 em]-x^3+2x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -x^{3}+2x = 0 } $, first we need to factor our $ x $.
$$ -x^{3}+2x = x \left( -x^{2}+2 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ -x^{2}+2 = 0$.
$ -x^{2}+2 = 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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