Solve for: 9x^2+4=-12x

Expression: $9{x}^{2}+4=-12x$

Move the variable to the left-hand side and change its sign


Use the commutative property to reorder the terms


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 $0$


Move the constant to the right-hand side and change its sign


Divide both sides of the equation by $3$

$\begin{align*}&x=-\frac{ 2 }{ 3 } \\&x=-0.\overset{ \cdot }{ 6 } \end{align*}$