N^2+N-48=-6

Solution for N^2+N-48=-6 equation:

Simplifying
N2 + N + -48 = -6

Reorder the terms:
-48 + N + N2 = -6

Solving
-48 + N + N2 = -6

Solving for variable 'N'.

Reorder the terms:
-48 + 6 + N + N2 = -6 + 6

Combine like terms: -48 + 6 = -42
-42 + N + N2 = -6 + 6

Combine like terms: -6 + 6 = 0
-42 + N + N2 = 0

Factor a trinomial.
(-7 + -1N)(6 + -1N) = 0

Subproblem 1
Set the factor '(-7 + -1N)' equal to zero and attempt to solve:

Simplifying
-7 + -1N = 0

Solving
-7 + -1N = 0

Move all terms containing N to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -1N = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1N = 0 + 7
-1N = 0 + 7

Combine like terms: 0 + 7 = 7
-1N = 7

Divide each side by '-1'.
N = -7

Simplifying
N = -7
Subproblem 2
Set the factor '(6 + -1N)' equal to zero and attempt to solve:

Simplifying
6 + -1N = 0

Solving
6 + -1N = 0

Move all terms containing N to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1N = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1N = 0 + -6
-1N = 0 + -6

Combine like terms: 0 + -6 = -6
-1N = -6

Divide each side by '-1'.
N = 6

Simplifying
N = 6
Solution
N = {-7, 6}