$$4y^3-9y = 0$$
Answer
$$ \begin{matrix}y_1 = 0 & y_2 = \dfrac{ 3 }{ 2 } & y_3 = -\dfrac{ 3 }{ 2 } \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ 4x^{3}-9x = 0 } $, first we need to factor our $ x $.
$$ 4x^{3}-9x = x \left( 4x^{2}-9 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 4x^{2}-9 = 0$.
$ 4x^{2}-9 = 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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