6n^2-18n-12=0

Solution for 6n^2-18n-12=0 equation:

Simplifying
6n2 + -18n + -12 = 0

Reorder the terms:
-12 + -18n + 6n2 = 0

Solving
-12 + -18n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + -3n + n2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-2 + -3n + n2)' equal to zero and attempt to solve:

Simplifying
-2 + -3n + n2 = 0

Solving
-2 + -3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3n + 2 + n2 = 0 + 2

Reorder the terms:
-2 + 2 + -3n + n2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3n + n2 = 0 + 2
-3n + n2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3n + n2 = 2

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 2 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3n + n2 = 4.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(n + -1.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
n + -1.5 = 2.061552813

Simplifying
n + -1.5 = 2.061552813

Reorder the terms:
-1.5 + n = 2.061552813

Solving
-1.5 + n = 2.061552813

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 2.061552813 + 1.5
n = 2.061552813 + 1.5

Combine like terms: 2.061552813 + 1.5 = 3.561552813
n = 3.561552813

Simplifying
n = 3.561552813

Subproblem 2
n + -1.5 = -2.061552813

Simplifying
n + -1.5 = -2.061552813

Reorder the terms:
-1.5 + n = -2.061552813

Solving
-1.5 + n = -2.061552813

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -2.061552813 + 1.5
n = -2.061552813 + 1.5

Combine like terms: -2.061552813 + 1.5 = -0.561552813
n = -0.561552813

Simplifying
n = -0.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.561552813, -0.561552813}
Solution
n = {3.561552813, -0.561552813}