Quadratic polynomial can be factored using the transformation $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$, where $x_{1}$ and $x_{2}$ are the solutions of the quadratic equation $ax^{2}+bx+c=0$.
$$-8y^{2}-12y=0$$
All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.
Now solve the equation $y=\frac{12±12}{-16}$ when $±$ is plus. Add $12$ to $12$.
$$y=\frac{24}{-16}$$
Reduce the fraction $\frac{24}{-16}$ to lowest terms by extracting and canceling out $8$.
$$y=-\frac{3}{2}$$
Now solve the equation $y=\frac{12±12}{-16}$ when $±$ is minus. Subtract $12$ from $12$.
$$y=\frac{0}{-16}$$
Divide $0$ by $-16$.
$$y=0$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $-\frac{3}{2}$ for $x_{1}$ and $0$ for $x_{2}$.
