In order to solve $ \color{blue}{ 15x^{3}-70x^{2}+80x = 0 } $, first we need to factor our $ x $.
$$ 15x^{3}-70x^{2}+80x = x \left( 15x^{2}-70x+80 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 15x^{2}-70x+80 = 0$.
$ 15x^{2}-70x+80 = 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.