6n^2+6n-177=3

Solution for 6n^2+6n-177=3 equation:

Simplifying
6n2 + 6n + -177 = 3

Reorder the terms:
-177 + 6n + 6n2 = 3

Solving
-177 + 6n + 6n2 = 3

Solving for variable 'n'.

Reorder the terms:
-177 + -3 + 6n + 6n2 = 3 + -3

Combine like terms: -177 + -3 = -180
-180 + 6n + 6n2 = 3 + -3

Combine like terms: 3 + -3 = 0
-180 + 6n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-30 + n + n2) = 0

Factor a trinomial.
6((-6 + -1n)(5 + -1n)) = 0

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

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 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 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

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

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-6, 5}