$$12n^3+8n^2+(-2n) = 0$$
Answer
$$ \begin{matrix}n_1 = 0 & n_2 = -\dfrac{ 1 }{ 3 }-\dfrac{\sqrt{ 10 }}{ 6 } & n_3 = -\dfrac{ 1 }{ 3 }+\dfrac{\sqrt{ 10 }}{ 6 } \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ 12x^{3}+8x^{2}-2x = 0 } $, first we need to factor our $ x $.
$$ 12x^{3}+8x^{2}-2x = x \left( 12x^{2}+8x-2 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 12x^{2}+8x-2 = 0$.
$ 12x^{2}+8x-2 = 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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