SOLUTION: If the sum of two consecutive integers is subtracted from their product, the result is 181. What are the two integers?

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Let the first integer be n, the next consecutive integer is n+1.
From the problem description, you can write:
Simplify and solve for n.

Solve this quadratic equation by factoring:
Apply the zero product principle:
and/or
If then and
If then and n+1 = 15
So you really get two pairs of integers which satisfy the given constraints and since the problem did not restrict the solution to positive integers only, you will have two answers:
14 and 15 is one pair.
-13 and -12 is the other pair.
Check:
= OK
= OK