$$11p^2 = 14p-3p^3$$
Answer
$$ \begin{matrix}p_1 = 0 & p_2 = 1 & p_3 = -\dfrac{ 14 }{ 3 } \end{matrix} $$
Explanation
$$ \begin{aligned} 11p^2 &= 14p-3p^3&& \text{simplify right side} \\[1 em]11p^2 &= -3p^3+14p&& \text{move all terms to the left hand side } \\[1 em]11p^2+3p^3-14p &= 0&& \text{simplify left side} \\[1 em]3p^3+11p^2-14p &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 3x^{3}+11x^{2}-14x = 0 } $, first we need to factor our $ x $.
$$ 3x^{3}+11x^{2}-14x = x \left( 3x^{2}+11x-14 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 3x^{2}+11x-14 = 0$.
$ 3x^{2}+11x-14 = 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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