$$x^2 = x^3$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 1 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2 &= x^3&& \text{move all terms to the left hand side } \\[1 em]x^2-x^3 &= 0&& \text{simplify left side} \\[1 em]-x^3+x^2 &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -x^{3}+x^{2} = 0 } $, first we need to factor our $ x^2 $.
$$ -x^{3}+x^{2} = x^2 \left( -x+1 \right) $$$ x = 0 $ is a root of multiplicity $ 2 $.
The second root can be found by solving equation $ -x+1 = 0$.
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