2N^2+2N-12=0

Solution for 2N^2+2N-12=0 equation:

Simplifying
2N2 + 2N + -12 = 0

Reorder the terms:
-12 + 2N + 2N2 = 0

Solving
-12 + 2N + 2N2 = 0

Solving for variable 'N'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + N + N2) = 0

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

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

Simplifying
-3 + -1N = 0

Solving
-3 + -1N = 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 + -1N = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1N = 0 + 3
-1N = 0 + 3

Combine like terms: 0 + 3 = 3
-1N = 3

Divide each side by '-1'.
N = -3

Simplifying
N = -3
Subproblem 2
Set the factor '(2 + -1N)' equal to zero and attempt to solve:

Simplifying
2 + -1N = 0

Solving
2 + -1N = 0

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

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

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

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

Divide each side by '-1'.
N = 2

Simplifying
N = 2
Solution
N = {-3, 2}