Question

The square of a number plus the number is 6
.

Answer 1

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.