Question
$$-3x^4+12x^3+8x+9x^4x^2+3x = 0$$
Answer
$$ x = 0 $$
Explanation
$$ \begin{aligned} -3x^4+12x^3+8x+9x^4x^2+3x &= 0&& \text{simplify left side} \\[1 em]-3x^4+12x^3+8x+9x^6+3x &= 0&& \\[1 em]9x^6-3x^4+12x^3+11x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 9x^{6}-3x^{4}+12x^{3}+11x = 0 } $, first we need to factor our $ x $.
$$ 9x^{6}-3x^{4}+12x^{3}+11x = x \left( 9x^{5}-3x^{3}+12x^{2}+11 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 9x^{5}-3x^{3}+12x^{2}+11 = 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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