SOLUTION: In solving the equation (x – 1)(x – 2) = 30, Eric stated that the solution would be x – 1 = 30 => x = 31 or(x – 2) = 30 => x = 32 However, at least one of these solutions fails

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Question 387696: In solving the equation (x – 1)(x – 2) = 30, Eric stated that the solution would be x – 1 = 30 => x = 31 or(x – 2) = 30 => x = 32
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 by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The solutions must work simultaneously,
%28x-1%29%28x-2%29=30
If x=31, then
%2831-1%29%2831-2%29=30
30%2829%29=30
29=1
So x=31 is not a solution.
Multiply out the left hand side using the FOIL method,
x%5E2-2x-x%2B2=30
x%5E2-3x-28=0
%28x-7%29%28x%2B4%29=0
Two solutions:
x-7=0
highlight%28x=7%29
.
.
x%2B4=0
highlight%28x=-4%29
So then,
%28x-1%29%28x-2%29=30
%287-1%29%287-2%29=30
%286%29%285%29=30
30=30
.
.
%28x-1%29%28x-2%29=30
%28-4-1%29%28-4-2%29=30
%28-5%29%28-6%29=30
30=30
Solutions verified.