3n^2+126=-39n

Solution for 3n^2+126=-39n equation:

Simplifying
3n2 + 126 = -39n

Reorder the terms:
126 + 3n2 = -39n

Solving
126 + 3n2 = -39n

Solving for variable 'n'.

Reorder the terms:
126 + 39n + 3n2 = -39n + 39n

Combine like terms: -39n + 39n = 0
126 + 39n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(42 + 13n + n2) = 0

Factor a trinomial.
3((7 + n)(6 + n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 0

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

Add '-7' to each side of the equation.
7 + -7 + n = 0 + -7

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

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

Simplifying
n = -7
Subproblem 2
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Solution
n = {-7, -6}