$$-2x(6x+2-x^5) = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -0.33403 & x_3 = -1.46744 \\[1 em] x_4 = 1.63921 & x_5 = 0.08113+1.57562i & x_6 = 0.08113-1.57562i \end{matrix} $$
Explanation
$$ \begin{aligned} -2x(6x+2-x^5) &= 0&& \text{simplify left side} \\[1 em]-(12x^2+4x-2x^6) &= 0&& \\[1 em]-12x^2-4x+2x^6 &= 0&& \\[1 em]2x^6-12x^2-4x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 2x^{6}-12x^{2}-4x = 0 } $, first we need to factor our $ x $.
$$ 2x^{6}-12x^{2}-4x = x \left( 2x^{5}-12x-4 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 2x^{5}-12x-4 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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