SAT Question 50e40f08: Nonlinear Functions answer and explanation with Desmos solution

The x-intercepts of a graph in the xy-plane are the points where $y=0$. Thus, for an x-intercept of the graph of $y=f\left(x\right)$, $0=f\left(x\right)$. Substituting $0$ for $f\left(x\right)$ in the equation $f\left(x\right)=\left(x+6\right)\left(x-4\right)$ yields $0=\left(x+6\right)\left(x-4\right)$. By the zero product property, $x+6=0$ and $x-4=0$. Subtracting $6$ from both sides of the equation $x+6=0$ yields $x=-6$. Adding $4$ to both sides of the equation $x-4=0$ yields $x=4$. Therefore, the x-coordinates of the x-intercepts of the graph of $y=f\left(x\right)$ are $-6$ and $4$. Note that -6 and 4 are examples of ways to enter a correct answer.