n = -6 or -3
Start by adding 18 + 9n to both sides. This gives you the classic quadratic equation that you can go to work on:
To factor this, your basic problem is to find factors a and b such that:
a * b = 18 and a+b = 9
You might have to do a little trial and error to find these. After awhile, it becomes second nature. 6 and 3 fit the bill.
And this basically is all there is to it! You can write:
(n+6)(n+3) = 0
...which is true when n = -6 or n = -3.