-12n^2-22n-8=0

Solution for -12n^2-22n-8=0 equation:

Simplifying
-12n2 + -22n + -8 = 0

Reorder the terms:
-8 + -22n + -12n2 = 0

Solving
-8 + -22n + -12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(4 + 11n + 6n2) = 0

Factor a trinomial.
-2((4 + 3n)(1 + 2n)) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(4 + 3n)' equal to zero and attempt to solve:

Simplifying
4 + 3n = 0

Solving
4 + 3n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3n = 0 + -4
3n = 0 + -4

Combine like terms: 0 + -4 = -4
3n = -4

Divide each side by '3'.
n = -1.333333333

Simplifying
n = -1.333333333
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 = {-1.333333333, -0.5}