n=(6n+3)(6n-4)

Solution for n=(6n+3)(6n-4) equation:

Simplifying
n = (6n + 3)(6n + -4)

Reorder the terms:
n = (3 + 6n)(6n + -4)

Reorder the terms:
n = (3 + 6n)(-4 + 6n)

Multiply (3 + 6n) * (-4 + 6n)
n = (3(-4 + 6n) + 6n * (-4 + 6n))
n = ((-4 * 3 + 6n * 3) + 6n * (-4 + 6n))
n = ((-12 + 18n) + 6n * (-4 + 6n))
n = (-12 + 18n + (-4 * 6n + 6n * 6n))
n = (-12 + 18n + (-24n + 36n2))

Combine like terms: 18n + -24n = -6n
n = (-12 + -6n + 36n2)

Solving
n = -12 + -6n + 36n2

Solving for variable 'n'.

Reorder the terms:
12 + n + 6n + -36n2 = -12 + -6n + 36n2 + 12 + 6n + -36n2

Combine like terms: n + 6n = 7n
12 + 7n + -36n2 = -12 + -6n + 36n2 + 12 + 6n + -36n2

Reorder the terms:
12 + 7n + -36n2 = -12 + 12 + -6n + 6n + 36n2 + -36n2

Combine like terms: -12 + 12 = 0
12 + 7n + -36n2 = 0 + -6n + 6n + 36n2 + -36n2
12 + 7n + -36n2 = -6n + 6n + 36n2 + -36n2

Combine like terms: -6n + 6n = 0
12 + 7n + -36n2 = 0 + 36n2 + -36n2
12 + 7n + -36n2 = 36n2 + -36n2

Combine like terms: 36n2 + -36n2 = 0
12 + 7n + -36n2 = 0

Begin completing the square.  Divide all terms by
-36 the coefficient of the squared term: 

Divide each side by '-36'.
-0.3333333333 + -0.1944444444n + n2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -0.1944444444n + 0.3333333333 + n2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -0.1944444444n + n2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -0.1944444444n + n2 = 0 + 0.3333333333
-0.1944444444n + n2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-0.1944444444n + n2 = 0.3333333333

The n term is -0.1944444444n.  Take half its coefficient (-0.0972222222).
Square it (0.009452160490) and add it to both sides.

Add '0.009452160490' to each side of the equation.
-0.1944444444n + 0.009452160490 + n2 = 0.3333333333 + 0.009452160490

Reorder the terms:
0.009452160490 + -0.1944444444n + n2 = 0.3333333333 + 0.009452160490

Combine like terms: 0.3333333333 + 0.009452160490 = 0.34278549379
0.009452160490 + -0.1944444444n + n2 = 0.34278549379

Factor a perfect square on the left side:
(n + -0.0972222222)(n + -0.0972222222) = 0.34278549379

Calculate the square root of the right side: 0.585478859

Break this problem into two subproblems by setting 
(n + -0.0972222222) equal to 0.585478859 and -0.585478859.

Subproblem 1
n + -0.0972222222 = 0.585478859

Simplifying
n + -0.0972222222 = 0.585478859

Reorder the terms:
-0.0972222222 + n = 0.585478859

Solving
-0.0972222222 + n = 0.585478859

Solving for variable 'n'.

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

Add '0.0972222222' to each side of the equation.
-0.0972222222 + 0.0972222222 + n = 0.585478859 + 0.0972222222

Combine like terms: -0.0972222222 + 0.0972222222 = 0.0000000000
0.0000000000 + n = 0.585478859 + 0.0972222222
n = 0.585478859 + 0.0972222222

Combine like terms: 0.585478859 + 0.0972222222 = 0.6827010812
n = 0.6827010812

Simplifying
n = 0.6827010812

Subproblem 2
n + -0.0972222222 = -0.585478859

Simplifying
n + -0.0972222222 = -0.585478859

Reorder the terms:
-0.0972222222 + n = -0.585478859

Solving
-0.0972222222 + n = -0.585478859

Solving for variable 'n'.

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

Add '0.0972222222' to each side of the equation.
-0.0972222222 + 0.0972222222 + n = -0.585478859 + 0.0972222222

Combine like terms: -0.0972222222 + 0.0972222222 = 0.0000000000
0.0000000000 + n = -0.585478859 + 0.0972222222
n = -0.585478859 + 0.0972222222

Combine like terms: -0.585478859 + 0.0972222222 = -0.4882566368
n = -0.4882566368

Simplifying
n = -0.4882566368

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.6827010812, -0.4882566368}