n^2=-7n-12

Solution for n^2=-7n-12 equation:

Simplifying
n2 = -7n + -12

Reorder the terms:
n2 = -12 + -7n

Solving
n2 = -12 + -7n

Solving for variable 'n'.

Reorder the terms:
12 + 7n + n2 = -12 + -7n + 12 + 7n

Reorder the terms:
12 + 7n + n2 = -12 + 12 + -7n + 7n

Combine like terms: -12 + 12 = 0
12 + 7n + n2 = 0 + -7n + 7n
12 + 7n + n2 = -7n + 7n

Combine like terms: -7n + 7n = 0
12 + 7n + n2 = 0

Factor a trinomial.
(4 + n)(3 + n) = 0

Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 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 + n = 0 + -3

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

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

Simplifying
n = -3
Solution
n = {-4, -3}