$$4x(x+3)(2x-1) = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = \dfrac{ 1 }{ 2 } & x_3 = -3 \end{matrix} $$
Explanation
$$ \begin{aligned} 4x(x+3)(2x-1) &= 0&& \text{simplify left side} \\[1 em](4x^2+12x)(2x-1) &= 0&& \\[1 em]8x^3-4x^2+24x^2-12x &= 0&& \\[1 em]8x^3+20x^2-12x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 8x^{3}+20x^{2}-12x = 0 } $, first we need to factor our $ x $.
$$ 8x^{3}+20x^{2}-12x = x \left( 8x^{2}+20x-12 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 8x^{2}+20x-12 = 0$.
$ 8x^{2}+20x-12 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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