2n^2-4n-12=0

Solution for 2n^2-4n-12=0 equation:

Simplifying
2n2 + -4n + -12 = 0

Reorder the terms:
-12 + -4n + 2n2 = 0

Solving
-12 + -4n + 2n2 = 0

Solving for variable 'n'.

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -2n + n2)' equal to zero and attempt to solve:

Simplifying
-6 + -2n + n2 = 0

Solving
-6 + -2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2n + 6 + n2 = 0 + 6

Reorder the terms:
-6 + 6 + -2n + n2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2n + n2 = 0 + 6
-2n + n2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2n + n2 = 6

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = 6 + 1

Reorder the terms:
1 + -2n + n2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2n + n2 = 7

Factor a perfect square on the left side:
(n + -1)(n + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(n + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1
n + -1 = 2.645751311

Simplifying
n + -1 = 2.645751311

Reorder the terms:
-1 + n = 2.645751311

Solving
-1 + n = 2.645751311

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = 2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + n = 2.645751311 + 1
n = 2.645751311 + 1

Combine like terms: 2.645751311 + 1 = 3.645751311
n = 3.645751311

Simplifying
n = 3.645751311

Subproblem 2
n + -1 = -2.645751311

Simplifying
n + -1 = -2.645751311

Reorder the terms:
-1 + n = -2.645751311

Solving
-1 + n = -2.645751311

Solving for variable 'n'.

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

Add '1' to each side of the equation.
-1 + 1 + n = -2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + n = -2.645751311 + 1
n = -2.645751311 + 1

Combine like terms: -2.645751311 + 1 = -1.645751311
n = -1.645751311

Simplifying
n = -1.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.645751311, -1.645751311}
Solution
n = {3.645751311, -1.645751311}