\(3x\left(2x+3\right)-4x^2=-9\)
\(3x\left(2x+3\right)-4x^2+9=0\)
\(3x\left(2x+3\right)-\left[\left(2x\right)^2-3^2\right]=0\)
\(3x\left(2x+3\right)-\left(2x-3\right)\left(2x+3\right)=0\)
\(\left(2x+3\right)\left(3x-2x+3\right)=0\)
\(\left(2x+3\right)\left(x+3\right)=0\)
\(\orbr{\begin{cases}2x+3=0\\x+3=0\end{cases}}\)
\(\orbr{\begin{cases}x=\frac{-3}{2}\\x=-3\end{cases}}\)