SAT Question 2926cc6d: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice C is correct. Since a product of two factors is equal to $0$ if and only if at least one of the factors is $0$, either $5x+4=0$ or $2x-5=0$. Subtracting $4$ from each side of the equation $5x+4=0$ yields $5x=-4$. Dividing each side of this equation by $5$ yields $x=-\frac{4}{5}$. Adding $5$ to each side of the equation $2x-5=0$ yields $2x=5$. Dividing each side of this equation by $2$ yields $x=\frac{5}{2}$. It follows that the solutions to the given equation are $-\frac{4}{5}$ and $\frac{5}{2}$. Therefore, $-\frac{4}{5}$ is a solution to the given equation.