\(\frac{4}{9}x^2+\frac{8}{3}x=0\)
\(\Rightarrow x\left(\frac{4}{9}x+\frac{8}{3}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\\frac{4}{9}x+\frac{8}{3}=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=0\\\frac{4}{9}x=-\frac{8}{3}\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=-6\end{cases}\left(tm\right)}\)