In order to solve $ \color{blue}{ -30x^{5}+5x^{3}-10x^{2} = 0 } $, first we need to factor our $ x^2 $.
$$ -30x^{5}+5x^{3}-10x^{2} = x^2 \left( -30x^{3}+5x-10 \right) $$$ x = 0 $ is a root of multiplicity $ 2 $.
The remaining roots can be found by solving equation $ -30x^{3}+5x-10 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.