2(n-8)n=-4(2n-1)

Solution for 2(n-8)n=-4(2n-1) equation:

Simplifying
2(n + -8) * n = -4(2n + -1)

Reorder the terms:
2(-8 + n) * n = -4(2n + -1)

Reorder the terms for easier multiplication:
2n(-8 + n) = -4(2n + -1)
(-8 * 2n + n * 2n) = -4(2n + -1)
(-16n + 2n2) = -4(2n + -1)

Reorder the terms:
-16n + 2n2 = -4(-1 + 2n)
-16n + 2n2 = (-1 * -4 + 2n * -4)
-16n + 2n2 = (4 + -8n)

Solving
-16n + 2n2 = 4 + -8n

Solving for variable 'n'.

Reorder the terms:
-4 + -16n + 8n + 2n2 = 4 + -8n + -4 + 8n

Combine like terms: -16n + 8n = -8n
-4 + -8n + 2n2 = 4 + -8n + -4 + 8n

Reorder the terms:
-4 + -8n + 2n2 = 4 + -4 + -8n + 8n

Combine like terms: 4 + -4 = 0
-4 + -8n + 2n2 = 0 + -8n + 8n
-4 + -8n + 2n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
-4 + -8n + 2n2 = 0

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

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

Simplifying
-2 + -4n + n2 = 0

Solving
-2 + -4n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4n + 2 + n2 = 0 + 2

Reorder the terms:
-2 + 2 + -4n + n2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -4n + n2 = 0 + 2
-4n + n2 = 0 + 2

Combine like terms: 0 + 2 = 2
-4n + n2 = 2

The n term is -4n.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4n + 4 + n2 = 2 + 4

Reorder the terms:
4 + -4n + n2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + -4n + n2 = 6

Factor a perfect square on the left side:
(n + -2)(n + -2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(n + -2) equal to 2.449489743 and -2.449489743.

Subproblem 1
n + -2 = 2.449489743

Simplifying
n + -2 = 2.449489743

Reorder the terms:
-2 + n = 2.449489743

Solving
-2 + n = 2.449489743

Solving for variable 'n'.

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

Add '2' to each side of the equation.
-2 + 2 + n = 2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + n = 2.449489743 + 2
n = 2.449489743 + 2

Combine like terms: 2.449489743 + 2 = 4.449489743
n = 4.449489743

Simplifying
n = 4.449489743

Subproblem 2
n + -2 = -2.449489743

Simplifying
n + -2 = -2.449489743

Reorder the terms:
-2 + n = -2.449489743

Solving
-2 + n = -2.449489743

Solving for variable 'n'.

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

Add '2' to each side of the equation.
-2 + 2 + n = -2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + n = -2.449489743 + 2
n = -2.449489743 + 2

Combine like terms: -2.449489743 + 2 = -0.449489743
n = -0.449489743

Simplifying
n = -0.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.449489743, -0.449489743}
Solution
n = {4.449489743, -0.449489743}