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

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) (Show Source): You can put this solution on YOUR website!
The solutions must work simultaneously,

If , then

So is not a solution.
Multiply out the left hand side using the FOIL method,

Two solutions:

.
.

So then,

.
.

Solutions verified.

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