n^2-n-13=-7

Solution for n^2-n-13=-7 equation:

Simplifying
n2 + -1n + -13 = -7

Reorder the terms:
-13 + -1n + n2 = -7

Solving
-13 + -1n + n2 = -7

Solving for variable 'n'.

Reorder the terms:
-13 + 7 + -1n + n2 = -7 + 7

Combine like terms: -13 + 7 = -6
-6 + -1n + n2 = -7 + 7

Combine like terms: -7 + 7 = 0
-6 + -1n + n2 = 0

Factor a trinomial.
(-2 + -1n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

Simplifying
n = -2
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-2, 3}