6n^2+144=-66n

Solution for 6n^2+144=-66n equation:

Simplifying
6n2 + 144 = -66n

Reorder the terms:
144 + 6n2 = -66n

Solving
144 + 6n2 = -66n

Solving for variable 'n'.

Reorder the terms:
144 + 66n + 6n2 = -66n + 66n

Combine like terms: -66n + 66n = 0
144 + 66n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(24 + 11n + n2) = 0

Factor a trinomial.
6((8 + n)(3 + n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + n = 0 + -8
n = 0 + -8

Combine like terms: 0 + -8 = -8
n = -8

Simplifying
n = -8
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 = {-8, -3}