$$30z^5-42z^2 = 0$$
Answer
$$ \begin{matrix}z_1 = 0 & z_2 = 1.11869 & z_3 = -0.55934+0.96881i \\[1 em] z_4 = -0.55934-0.96881i & \\[1 em] \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ 30x^{5}-42x^{2} = 0 } $, first we need to factor our $ x^2 $.
$$ 30x^{5}-42x^{2} = x^2 \left( 30x^{3}-42 \right) $$$ x = 0 $ is a root of multiplicity $ 2 $.
The remaining roots can be found by solving equation $ 30x^{3}-42 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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