In order to solve $ \color{blue}{ -4x^{3}+100x = 0 } $, first we need to factor our $ x $.
$$ -4x^{3}+100x = x \left( -4x^{2}+100 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ -4x^{2}+100 = 0$.
$ -4x^{2}+100 = 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.