The square of a number plus the number is 6

.

N^2 + n = 6, or n^2 + n - 6 = 0

Factor this, and set each factor = 0 separately, and solve for n in each case:

(n+3) (n-2) = 0.

Then n=-3 amd n=2. It's very important that you check both answers and determine for yourself whether or not they make sense.