8n^2+68n+117=-3

Solution for 8n^2+68n+117=-3 equation:

Simplifying
8n2 + 68n + 117 = -3

Reorder the terms:
117 + 68n + 8n2 = -3

Solving
117 + 68n + 8n2 = -3

Solving for variable 'n'.

Reorder the terms:
117 + 3 + 68n + 8n2 = -3 + 3

Combine like terms: 117 + 3 = 120
120 + 68n + 8n2 = -3 + 3

Combine like terms: -3 + 3 = 0
120 + 68n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + 17n + 2n2) = 0

Factor a trinomial.
4((6 + n)(5 + 2n)) = 0

Ignore the factor 4.
Subproblem 1
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
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 = {-6, -2.5}