In solving the equation (x + 4)(x – 7) = -24, Eric stated that the solution would be
x + 4 = -24 = x = -28
or
(x – 7) = -24 = x = -17
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning

Question

In solving the equation (x + 4)(x – 7) = -24, Eric stated that the solution would be
x + 4 = -24 => x = -28
or
(x – 7) = -24 => x = -17
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning

myininaya · Answer

If you have a*b=-24, this doesn't mean a=-24 or b=-24 of both=-24
Think of all the factors of -24.
What is possible for a and b to be?