Question

In solving the equation (x + 1)(x – 2) = 54, Eric stated that the solution would be
x + 1 = 54 => x = 53
or
(x – 2) = 54 => x = 56
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.

Answer 1

(x+1)(x-2)=54
use FOIL to x^2 - x -2 =54

so x^2 - x -56 =0
x^2-8x+7x-56=0
x(x-8) +7(x-8)=
(x-8)(x+7)=0
so x-8=0 or x+7=0
hence x=8 or x=-7

Answer 2

he is using the zero-product property.
However, the zero-product property only applies if the product is zero.