12n^2+66n+88=-2

Solution for 12n^2+66n+88=-2 equation:

Simplifying
12n2 + 66n + 88 = -2

Reorder the terms:
88 + 66n + 12n2 = -2

Solving
88 + 66n + 12n2 = -2

Solving for variable 'n'.

Reorder the terms:
88 + 2 + 66n + 12n2 = -2 + 2

Combine like terms: 88 + 2 = 90
90 + 66n + 12n2 = -2 + 2

Combine like terms: -2 + 2 = 0
90 + 66n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(15 + 11n + 2n2) = 0

Factor a trinomial.
6((3 + n)(5 + 2n)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + 2n)' equal to zero and attempt to solve:

Simplifying
5 + 2n = 0

Solving
5 + 2n = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2n = 0 + -5
2n = 0 + -5

Combine like terms: 0 + -5 = -5
2n = -5

Divide each side by '2'.
n = -2.5

Simplifying
n = -2.5
Solution
n = {-3, -2.5}