$\begin{array}{l}
4 x^{2}+5 x=0 \\
\Rightarrow x(4 x+5)=0 \\
\Rightarrow x=0 \text { or } 4 x+5=0
\end{array}$
$\Rightarrow x=0$ or $x=-\frac{5}{4}$

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