$$x^2(x-\frac{1^1}{2}) = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = \dfrac{ 1 }{ 2 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2(x-\frac{1^1}{2}) &= 0&& \text{simplify left side} \\[1 em]x^2(x-\frac{1}{2}) &= 0&& \\[1 em]x^2\frac{2x-1}{2} &= 0&& \\[1 em]\frac{2x^3-x^2}{2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{2x^3-x^2}{2} &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]2x^3-x^2 &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 2x^{3}-x^{2} = 0 } $, first we need to factor our $ x^2 $.
$$ 2x^{3}-x^{2} = x^2 \left( 2x-1 \right) $$$ x = 0 $ is a root of multiplicity $ 2 $.
The second root can be found by solving equation $ 2x-1 = 0$.
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