8n^2+16n+12=6

Solution for 8n^2+16n+12=6 equation:

Simplifying
8n2 + 16n + 12 = 6

Reorder the terms:
12 + 16n + 8n2 = 6

Solving
12 + 16n + 8n2 = 6

Solving for variable 'n'.

Reorder the terms:
12 + -6 + 16n + 8n2 = 6 + -6

Combine like terms: 12 + -6 = 6
6 + 16n + 8n2 = 6 + -6

Combine like terms: 6 + -6 = 0
6 + 16n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 8n + 4n2) = 0

Factor a trinomial.
2((3 + 2n)(1 + 2n)) = 0

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

Simplifying
3 + 2n = 0

Solving
3 + 2n = 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 + 2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2n = 0 + -3
2n = 0 + -3

Combine like terms: 0 + -3 = -3
2n = -3

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
Subproblem 2
Set the factor '(1 + 2n)' equal to zero and attempt to solve:

Simplifying
1 + 2n = 0

Solving
1 + 2n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2n = 0 + -1
2n = 0 + -1

Combine like terms: 0 + -1 = -1
2n = -1

Divide each side by '2'.
n = -0.5

Simplifying
n = -0.5
Solution
n = {-1.5, -0.5}