6n^2-18n-18=16

Solution for 6n^2-18n-18=16 equation:

Simplifying
6n2 + -18n + -18 = 16

Reorder the terms:
-18 + -18n + 6n2 = 16

Solving
-18 + -18n + 6n2 = 16

Solving for variable 'n'.

Reorder the terms:
-18 + -16 + -18n + 6n2 = 16 + -16

Combine like terms: -18 + -16 = -34
-34 + -18n + 6n2 = 16 + -16

Combine like terms: 16 + -16 = 0
-34 + -18n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + -9n + 3n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + -9n + 3n2)' equal to zero and attempt to solve:

Simplifying
-17 + -9n + 3n2 = 0

Solving
-17 + -9n + 3n2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-5.666666667 + -3n + n2 = 0

Move the constant term to the right:

Add '5.666666667' to each side of the equation.
-5.666666667 + -3n + 5.666666667 + n2 = 0 + 5.666666667

Reorder the terms:
-5.666666667 + 5.666666667 + -3n + n2 = 0 + 5.666666667

Combine like terms: -5.666666667 + 5.666666667 = 0.000000000
0.000000000 + -3n + n2 = 0 + 5.666666667
-3n + n2 = 0 + 5.666666667

Combine like terms: 0 + 5.666666667 = 5.666666667
-3n + n2 = 5.666666667

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 = 5.666666667 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 5.666666667 + 2.25

Combine like terms: 5.666666667 + 2.25 = 7.916666667
2.25 + -3n + n2 = 7.916666667

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 7.916666667

Calculate the square root of the right side: 2.813657169

Break this problem into two subproblems by setting 
(n + -1.5) equal to 2.813657169 and -2.813657169.

Subproblem 1
n + -1.5 = 2.813657169

Simplifying
n + -1.5 = 2.813657169

Reorder the terms:
-1.5 + n = 2.813657169

Solving
-1.5 + n = 2.813657169

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 = 2.813657169 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 2.813657169 + 1.5
n = 2.813657169 + 1.5

Combine like terms: 2.813657169 + 1.5 = 4.313657169
n = 4.313657169

Simplifying
n = 4.313657169

Subproblem 2
n + -1.5 = -2.813657169

Simplifying
n + -1.5 = -2.813657169

Reorder the terms:
-1.5 + n = -2.813657169

Solving
-1.5 + n = -2.813657169

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 = -2.813657169 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -2.813657169 + 1.5
n = -2.813657169 + 1.5

Combine like terms: -2.813657169 + 1.5 = -1.313657169
n = -1.313657169

Simplifying
n = -1.313657169

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.313657169, -1.313657169}
Solution
n = {4.313657169, -1.313657169}