4n^2-4n=64

Solution for 4n^2-4n=64 equation:

Simplifying
4n2 + -4n = 64

Reorder the terms:
-4n + 4n2 = 64

Solving
-4n + 4n2 = 64

Solving for variable 'n'.

Reorder the terms:
-64 + -4n + 4n2 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + -4n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + -1n + n2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-16 + -1n + n2)' equal to zero and attempt to solve:

Simplifying
-16 + -1n + n2 = 0

Solving
-16 + -1n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -1n + 16 + n2 = 0 + 16

Reorder the terms:
-16 + 16 + -1n + n2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1n + n2 = 0 + 16
-1n + n2 = 0 + 16

Combine like terms: 0 + 16 = 16
-1n + n2 = 16

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = 16 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 16 + 0.25

Combine like terms: 16 + 0.25 = 16.25
0.25 + -1n + n2 = 16.25

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(n + -0.5) equal to 4.031128874 and -4.031128874.

Subproblem 1
n + -0.5 = 4.031128874

Simplifying
n + -0.5 = 4.031128874

Reorder the terms:
-0.5 + n = 4.031128874

Solving
-0.5 + n = 4.031128874

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = 4.031128874 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 4.031128874 + 0.5
n = 4.031128874 + 0.5

Combine like terms: 4.031128874 + 0.5 = 4.531128874
n = 4.531128874

Simplifying
n = 4.531128874

Subproblem 2
n + -0.5 = -4.031128874

Simplifying
n + -0.5 = -4.031128874

Reorder the terms:
-0.5 + n = -4.031128874

Solving
-0.5 + n = -4.031128874

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = -4.031128874 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -4.031128874 + 0.5
n = -4.031128874 + 0.5

Combine like terms: -4.031128874 + 0.5 = -3.531128874
n = -3.531128874

Simplifying
n = -3.531128874

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.531128874, -3.531128874}
Solution
n = {4.531128874, -3.531128874}