If \(8\) and \(-4\) are the solutions for \(x\), then the factors of the equation will be \((x-8) \)and \((x+4) \)

and the factorized form of the equation will be

\((x-8)(x+4) = 0\)

Clearly, the constant term will be \(-32\) and only choice A has the equation with the constant term \(-32\)

Hence, Choice A is the correct answer.

Actually, we don't have to go this far. Since the solutions \(8\) and \(-4\) are of opposite signs, the constants in the linear factors of the equation will also be of opposite signs and their product will be negative. We simply have to look for equations with \(-32\) amongst the choices and there is only one, Choice A.