=n^2+7n+12

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

Simplifying
0 = n2 + 7n + 12

Reorder the terms:
0 = 12 + 7n + n2

Solving
0 = 12 + 7n + n2

Solving for variable 'n'.

Combine like terms: 0 + -12 = -12
-12 + -7n + -1n2 = 12 + 7n + n2 + -12 + -7n + -1n2

Reorder the terms:
-12 + -7n + -1n2 = 12 + -12 + 7n + -7n + n2 + -1n2

Combine like terms: 12 + -12 = 0
-12 + -7n + -1n2 = 0 + 7n + -7n + n2 + -1n2
-12 + -7n + -1n2 = 7n + -7n + n2 + -1n2

Combine like terms: 7n + -7n = 0
-12 + -7n + -1n2 = 0 + n2 + -1n2
-12 + -7n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-12 + -7n + -1n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 7n + n2) = 0

Factor a trinomial.
-1((4 + n)(3 + n)) = 0

Ignore the factor -1.
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}