SAT Question 717a1964: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

The left-hand side of the given equation can be rewritten by factoring. The two values that multiply to $-24$ and add to $10$ are $12$ and $-2$. It follows that the given equation can be rewritten as $\left(z+12\right)\left(z-2\right)=0$. Setting each factor equal to $0$ yields two equations: $z+12=0$ and $z-2=0$. Subtracting $12$ from both sides of the equation $z+12=0$ results in $z=-12$. Adding $2$ to both sides of the equation $z-2=0$ results in $z=2$. Note that 2 and -12 are examples of ways to enter a correct answer.