#### Answer

{-9, 8}

#### Work Step by Step

Reorder $n^{2}$ + n = 72 to $n^{2}$ + n - 72
1. Factor:
$n^{2}$ + n - 72 = (n + 9)(n - 8)
2. Apply the zero factor property to the factored expression:
a) n + 9 = 0
b) n - 8 = 0
3. Solve each linear equation:
a) n = -9
b) n = 8
The solutions are {-9, 8}.