$$3x^6+4x^5+3x^4+3x^2+2x = 0$$

$$ \begin{matrix}x_1 = 0 & x_2 = -0.56474 & x_3 = 0.50175+0.69328i \\[1 em] x_4 = 0.50175-0.69328i & x_5 = -0.88605+0.90926i & x_6 = -0.88605-0.90926i \end{matrix} $$

In order to solve $ \color{blue}{ 3x^{6}+4x^{5}+3x^{4}+3x^{2}+2x = 0 } $, first we need to factor our $ x $.

$$ 3x^{6}+4x^{5}+3x^{4}+3x^{2}+2x = x \left( 3x^{5}+4x^{4}+3x^{3}+3x+2 \right) $$

$ x = 0 $ is a root of multiplicity $ 1 $.

The remaining roots can be found by solving equation $ 3x^{5}+4x^{4}+3x^{3}+3x+2 = 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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