Solve each of the following quadratic equations:

$4 x^{2}+5 x=0$

$\Rightarrow x(4 x+5)=0$

$\Rightarrow x=0$ or $4 x+5=0$

$\Rightarrow x=0$ or $x=-\frac{5}{4}$

Hence, the roots of the given equation are 0 and $-\frac{5}{4}$.