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