$$0 = x^3+3x^2-5x$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = -\dfrac{ 3 }{ 2 }-\dfrac{\sqrt{ 29 }}{ 2 } & x_3 = -\dfrac{ 3 }{ 2 }+\dfrac{\sqrt{ 29 }}{ 2 } \end{matrix} $$
Explanation
$$ \begin{aligned} 0 &= x^3+3x^2-5x&& \text{move all terms to the left hand side } \\[1 em]0-x^3-3x^2+5x &= 0&& \text{simplify left side} \\[1 em]-x^3-3x^2+5x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -x^{3}-3x^{2}+5x = 0 } $, first we need to factor our $ x $.
$$ -x^{3}-3x^{2}+5x = x \left( -x^{2}-3x+5 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ -x^{2}-3x+5 = 0$.
$ -x^{2}-3x+5 = 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.
This page was created using
Polynomial Equations Solver