3n^2+12=-12n

Solution for 3n^2+12=-12n equation:

Simplifying
3n2 + 12 = -12n

Reorder the terms:
12 + 3n2 = -12n

Solving
12 + 3n2 = -12n

Solving for variable 'n'.

Reorder the terms:
12 + 12n + 3n2 = -12n + 12n

Combine like terms: -12n + 12n = 0
12 + 12n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 4n + n2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 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 + n = 0 + -2

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

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

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

Simplifying
2 + n = 0

Solving
2 + n = 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 + n = 0 + -2

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

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

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