(2n+2)(6n+1)=9

Solution for (2n+2)(6n+1)=9 equation:

Simplifying
(2n + 2)(6n + 1) = 9

Reorder the terms:
(2 + 2n)(6n + 1) = 9

Reorder the terms:
(2 + 2n)(1 + 6n) = 9

Multiply (2 + 2n) * (1 + 6n)
(2(1 + 6n) + 2n * (1 + 6n)) = 9
((1 * 2 + 6n * 2) + 2n * (1 + 6n)) = 9
((2 + 12n) + 2n * (1 + 6n)) = 9
(2 + 12n + (1 * 2n + 6n * 2n)) = 9
(2 + 12n + (2n + 12n2)) = 9

Combine like terms: 12n + 2n = 14n
(2 + 14n + 12n2) = 9

Solving
2 + 14n + 12n2 = 9

Solving for variable 'n'.

Reorder the terms:
2 + -9 + 14n + 12n2 = 9 + -9

Combine like terms: 2 + -9 = -7
-7 + 14n + 12n2 = 9 + -9

Combine like terms: 9 + -9 = 0
-7 + 14n + 12n2 = 0

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

Divide each side by '12'.
-0.5833333333 + 1.166666667n + n2 = 0

Move the constant term to the right:

Add '0.5833333333' to each side of the equation.
-0.5833333333 + 1.166666667n + 0.5833333333 + n2 = 0 + 0.5833333333

Reorder the terms:
-0.5833333333 + 0.5833333333 + 1.166666667n + n2 = 0 + 0.5833333333

Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000
0.0000000000 + 1.166666667n + n2 = 0 + 0.5833333333
1.166666667n + n2 = 0 + 0.5833333333

Combine like terms: 0 + 0.5833333333 = 0.5833333333
1.166666667n + n2 = 0.5833333333

The n term is 1.166666667n.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667n + 0.3402777780 + n2 = 0.5833333333 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667n + n2 = 0.5833333333 + 0.3402777780

Combine like terms: 0.5833333333 + 0.3402777780 = 0.9236111113
0.3402777780 + 1.166666667n + n2 = 0.9236111113

Factor a perfect square on the left side:
(n + 0.5833333335)(n + 0.5833333335) = 0.9236111113

Calculate the square root of the right side: 0.961046883

Break this problem into two subproblems by setting 
(n + 0.5833333335) equal to 0.961046883 and -0.961046883.

Subproblem 1
n + 0.5833333335 = 0.961046883

Simplifying
n + 0.5833333335 = 0.961046883

Reorder the terms:
0.5833333335 + n = 0.961046883

Solving
0.5833333335 + n = 0.961046883

Solving for variable 'n'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + n = 0.961046883 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + n = 0.961046883 + -0.5833333335
n = 0.961046883 + -0.5833333335

Combine like terms: 0.961046883 + -0.5833333335 = 0.3777135495
n = 0.3777135495

Simplifying
n = 0.3777135495

Subproblem 2
n + 0.5833333335 = -0.961046883

Simplifying
n + 0.5833333335 = -0.961046883

Reorder the terms:
0.5833333335 + n = -0.961046883

Solving
0.5833333335 + n = -0.961046883

Solving for variable 'n'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + n = -0.961046883 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + n = -0.961046883 + -0.5833333335
n = -0.961046883 + -0.5833333335

Combine like terms: -0.961046883 + -0.5833333335 = -1.5443802165
n = -1.5443802165

Simplifying
n = -1.5443802165

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.3777135495, -1.5443802165}