$9{x}^{2}+4+12x=0$
Use the commutative property to reorder the terms$9{x}^{2}+12x+4=0$
Use ${a}^{2}+2ab+{b}^{2}={\left( a+b \right)}^{2}$ to factor the expression${\left( 3x+2 \right)}^{2}=0$
The only way a power can be $0$ is when the base equals $0$$3x+2=0$
Move the constant to the right-hand side and change its sign$3x=-2$
Divide both sides of the equation by $3$$\begin{align*}&x=-\frac{ 2 }{ 3 } \\&x=-0.\overset{ \cdot }{ 6 } \end{align*}$