If you solve n^2 - 8n - 48 = 0 by factoring, you'd do this:
1. What multplies to make -48?
1 (-48)
2 (-24)
3 (-16)
4 (-12)
6 (-8)
2. Which of those adds to make -8?
4 + (-12) =-8
3. So n^2 - 8n - 48 = 0 factors as (n+4)(n-12) = 0
4. Set each factor equal to 0
n+4 = 0 or n-12 = 0
n = -4 n = 12
The two solutions are -4 and 12.
