*Before I begin, I am not sure why there are two different variables, they should both be the same. So, I am just going to use n as the variable
Set the equation up so that it equals zero. To do that, add 15 on both sides of the equation
n² + 8n + 15 = 0
Now, to factor, find 2 numbers that multiply to get 15, but also add up to get 8
The 2 numbers that multiply to get 15 are 3 and 5. 3 and 5 also add up to get 8
Now, put 3 and 5 into 2 sets of parenthesis
(n + 3)(n + 5)
Now, you can set each set of parenthesis equal to zero and solve
n + 3 = 0
Subtract 3 on both sides of the equation
n = -3
Set the other set of parenthesis equal to zero
n + 5 = 0
Subtract 5
n = -5
So, n= -3 and n= -5