Question
$$4x^4-2+x^2+3x+2+4x^4-2+x^2+3x+2 = 0$$
Answer
$$ x = 0 $$
Explanation
$$ \begin{aligned} 4x^4-2+x^2+3x+2+4x^4-2+x^2+3x+2 &= 0&& \text{simplify left side} \\[1 em]4x^4-2+x^2+3x+2+4x^4-2+x^2+3x+2 &= 0&& \\[1 em]8x^4+2x^2+6x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 8x^{4}+2x^{2}+6x = 0 } $, first we need to factor our $ x $.
$$ 8x^{4}+2x^{2}+6x = x \left( 8x^{3}+2x+6 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 8x^{3}+2x+6 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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