Translating into a mathematical equation:
n + n^2 = 72
Rewriting, n^2 + n - 72 = 0
Factoring, (n+9)(n-8) = 0
Solving for n: n = -9 or n = 8
You must check both answers before accepting one, the other or both.
Example: suppose we check out n = 8. Then 8 + 8^2 = 72 is true, and n = 8 is a solution. Is n = -9 a solution? Try it.