$$(20x-2x^2)(10x-2x^2) = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 5 & x_3 = 10 \end{matrix} $$
Explanation
$$ \begin{aligned} (20x-2x^2)(10x-2x^2) &= 0&& \text{simplify left side} \\[1 em]200x^2-40x^3-20x^3+4x^4 &= 0&& \\[1 em]4x^4-60x^3+200x^2 &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 4x^{4}-60x^{3}+200x^{2} = 0 } $, first we need to factor our $ x^2 $.
$$ 4x^{4}-60x^{3}+200x^{2} = x^2 \left( 4x^{2}-60x+200 \right) $$$ x = 0 $ is a root of multiplicity $ 2 $.
The remaining roots can be found by solving equation $ 4x^{2}-60x+200 = 0$.
$ 4x^{2}-60x+200 = 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
Equations Solver