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