$$-x^5+5x^3-2x = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 0.66215 & x_3 = -0.66215 \\[1 em] x_4 = -2.13578 & x_5 = 2.13578 \\[1 em] \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ -x^{5}+5x^{3}-2x = 0 } $, first we need to factor our $ x $.
$$ -x^{5}+5x^{3}-2x = x \left( -x^{4}+5x^{2}-2 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ -x^{4}+5x^{2}-2 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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