12-2n=8(n+4)n

Solution for 12-2n=8(n+4)n equation:

Simplifying
12 + -2n = 8(n + 4) * n

Reorder the terms:
12 + -2n = 8(4 + n) * n

Reorder the terms for easier multiplication:
12 + -2n = 8n(4 + n)
12 + -2n = (4 * 8n + n * 8n)
12 + -2n = (32n + 8n2)

Solving
12 + -2n = 32n + 8n2

Solving for variable 'n'.

Combine like terms: -2n + -32n = -34n
12 + -34n + -8n2 = 32n + 8n2 + -32n + -8n2

Reorder the terms:
12 + -34n + -8n2 = 32n + -32n + 8n2 + -8n2

Combine like terms: 32n + -32n = 0
12 + -34n + -8n2 = 0 + 8n2 + -8n2
12 + -34n + -8n2 = 8n2 + -8n2

Combine like terms: 8n2 + -8n2 = 0
12 + -34n + -8n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -17n + -4n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -17n + -4n2)' equal to zero and attempt to solve:

Simplifying
6 + -17n + -4n2 = 0

Solving
6 + -17n + -4n2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.5 + 4.25n + n2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 4.25n + 1.5 + n2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 4.25n + n2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 4.25n + n2 = 0 + 1.5
4.25n + n2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
4.25n + n2 = 1.5

The n term is 4.25n.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25n + 4.515625 + n2 = 1.5 + 4.515625

Reorder the terms:
4.515625 + 4.25n + n2 = 1.5 + 4.515625

Combine like terms: 1.5 + 4.515625 = 6.015625
4.515625 + 4.25n + n2 = 6.015625

Factor a perfect square on the left side:
(n + 2.125)(n + 2.125) = 6.015625

Calculate the square root of the right side: 2.452677109

Break this problem into two subproblems by setting 
(n + 2.125) equal to 2.452677109 and -2.452677109.

Subproblem 1
n + 2.125 = 2.452677109

Simplifying
n + 2.125 = 2.452677109

Reorder the terms:
2.125 + n = 2.452677109

Solving
2.125 + n = 2.452677109

Solving for variable 'n'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + n = 2.452677109 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + n = 2.452677109 + -2.125
n = 2.452677109 + -2.125

Combine like terms: 2.452677109 + -2.125 = 0.327677109
n = 0.327677109

Simplifying
n = 0.327677109

Subproblem 2
n + 2.125 = -2.452677109

Simplifying
n + 2.125 = -2.452677109

Reorder the terms:
2.125 + n = -2.452677109

Solving
2.125 + n = -2.452677109

Solving for variable 'n'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + n = -2.452677109 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + n = -2.452677109 + -2.125
n = -2.452677109 + -2.125

Combine like terms: -2.452677109 + -2.125 = -4.577677109
n = -4.577677109

Simplifying
n = -4.577677109

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.327677109, -4.577677109}
Solution
n = {0.327677109, -4.577677109}