-8n(8n-8)=8

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Solution for -8n(8n-8)=8 equation: 


Simplifying
-8n(8n + -8) = 8

Reorder the terms:
-8n(-8 + 8n) = 8
(-8 * -8n + 8n * -8n) = 8
(64n + -64n2) = 8

Solving
64n + -64n2 = 8

Solving for variable 'n'.

Reorder the terms:
-8 + 64n + -64n2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 64n + -64n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-1 + 8n + -8n2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-1 + 8n + -8n2)' equal to zero and attempt to solve:

Simplifying
-1 + 8n + -8n2 = 0

Solving
-1 + 8n + -8n2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
0.125 + -1n + n2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -1n + -0.125 + n2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -1n + n2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -1n + n2 = 0 + -0.125
-1n + n2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-1n + n2 = -0.125

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 = -0.125 + 0.25

Reorder the terms:
0.25 + -1n + n2 = -0.125 + 0.25

Combine like terms: -0.125 + 0.25 = 0.125
0.25 + -1n + n2 = 0.125

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(n + -0.5) equal to 0.353553391 and -0.353553391.


Subproblem 1
n + -0.5 = 0.353553391

Simplifying
n + -0.5 = 0.353553391

Reorder the terms:
-0.5 + n = 0.353553391

Solving
-0.5 + n = 0.353553391

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 = 0.353553391 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 0.353553391 + 0.5
n = 0.353553391 + 0.5

Combine like terms: 0.353553391 + 0.5 = 0.853553391
n = 0.853553391

Simplifying
n = 0.853553391


Subproblem 2
n + -0.5 = -0.353553391

Simplifying
n + -0.5 = -0.353553391

Reorder the terms:
-0.5 + n = -0.353553391

Solving
-0.5 + n = -0.353553391

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 = -0.353553391 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -0.353553391 + 0.5
n = -0.353553391 + 0.5

Combine like terms: -0.353553391 + 0.5 = 0.146446609
n = 0.146446609

Simplifying
n = 0.146446609


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.853553391, 0.146446609}
Solution
n = {0.853553391, 0.146446609}

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