SAT Question 7028c74f: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Subtracting $5\left(x+7\right)$ from each side of the given equation yields $0=15\left(x-17\right)\left(x+7\right)-5\left(x+7\right)$. Since $5\left(x+7\right)$ is a common factor of each of the terms on the right-hand side of this equation, it can be rewritten as $0=5\left(x+7\right)\left(3\left(x-17\right)-1\right)$. This is equivalent to $0=5\left(x+7\right)\left(3x-51-1\right)$, or $0=5\left(x+7\right)\left(3x-52\right)$. Dividing both sides of this equation by $5$ yields $0=\left(x+7\right)\left(3x-52\right)$. Since a product of two factors is equal to $0$ if and only if at least one of the factors is $0$, either $x+7=0$ or $3x-52=0$. Subtracting $7$ from both sides of the equation $x+7=0$ yields $x=-7$. Adding $52$ to both sides of the equation $3x-52=0$ yields $3x=52$. Dividing both sides of this equation by $3$ yields $x=\frac{52}{3}$. Therefore, the solutions to the given equation are $-7$ and $\frac{52}{3}$. It follows that the sum of the solutions to the given equation is $-7+\frac{52}{3}$, which is equivalent to $-\frac{21}{3}+\frac{52}{3}$, or $\frac{31}{3}$. Note that 31/3 and 10.33 are examples of ways to enter a correct answer.