Answer
$z=0$ or $z=\sqrt[3]{\frac{5}{2}}$
Work Step by Step
We solve by factoring:
$4z^{5}-10z^{2}=0$
$2z^{2}(2z^{3}-5)=0$
$2z^{2}=0$ or $2z^{3}-5=0$
$z^2=0$ or $z^3=5/2$
$z=0$ or $z=\sqrt[3]{\frac{5}{2}}$
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