SAT Question c81b6c57: Equivalent Expressions answer and explanation with Desmos solution

Choice B is correct. Using the distributive property, the first given expression can be rewritten as $6x^2+3px+24-16px-64x$, and then rewritten as $6x^2+(3p-16p-64)x+24$. Since the expression $6x^2+(3p-16p-64)x+24$ is equivalent to $6x^2-155x+24$, the coefficients of the $x$-terms from each expression are equivalent to each other; thus $3p-16p-64=-155$. Combining like terms gives $-13p-64=-155$. Adding $64$ to both sides of the equation gives $-13p=-91$. Dividing both sides of the equation by $-13$ yields $p=7$.