-8n(1-8n)-2(n+3)=

Solution for -8n(1-8n)-2(n+3)= equation:

Simplifying
-8n(1 + -8n) + -2(n + 3) = 0
(1 * -8n + -8n * -8n) + -2(n + 3) = 0
(-8n + 64n2) + -2(n + 3) = 0

Reorder the terms:
-8n + 64n2 + -2(3 + n) = 0
-8n + 64n2 + (3 * -2 + n * -2) = 0
-8n + 64n2 + (-6 + -2n) = 0

Reorder the terms:
-6 + -8n + -2n + 64n2 = 0

Combine like terms: -8n + -2n = -10n
-6 + -10n + 64n2 = 0

Solving
-6 + -10n + 64n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5n + 32n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -5n + 32n2)' equal to zero and attempt to solve:

Simplifying
-3 + -5n + 32n2 = 0

Solving
-3 + -5n + 32n2 = 0

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

Divide each side by '32'.
-0.09375 + -0.15625n + n2 = 0

Move the constant term to the right:

Add '0.09375' to each side of the equation.
-0.09375 + -0.15625n + 0.09375 + n2 = 0 + 0.09375

Reorder the terms:
-0.09375 + 0.09375 + -0.15625n + n2 = 0 + 0.09375

Combine like terms: -0.09375 + 0.09375 = 0.00000
0.00000 + -0.15625n + n2 = 0 + 0.09375
-0.15625n + n2 = 0 + 0.09375

Combine like terms: 0 + 0.09375 = 0.09375
-0.15625n + n2 = 0.09375

The n term is -0.15625n.  Take half its coefficient (-0.078125).
Square it (0.006103515625) and add it to both sides.

Add '0.006103515625' to each side of the equation.
-0.15625n + 0.006103515625 + n2 = 0.09375 + 0.006103515625

Reorder the terms:
0.006103515625 + -0.15625n + n2 = 0.09375 + 0.006103515625

Combine like terms: 0.09375 + 0.006103515625 = 0.099853515625
0.006103515625 + -0.15625n + n2 = 0.099853515625

Factor a perfect square on the left side:
(n + -0.078125)(n + -0.078125) = 0.099853515625

Calculate the square root of the right side: 0.315996069

Break this problem into two subproblems by setting 
(n + -0.078125) equal to 0.315996069 and -0.315996069.

Subproblem 1
n + -0.078125 = 0.315996069

Simplifying
n + -0.078125 = 0.315996069

Reorder the terms:
-0.078125 + n = 0.315996069

Solving
-0.078125 + n = 0.315996069

Solving for variable 'n'.

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

Add '0.078125' to each side of the equation.
-0.078125 + 0.078125 + n = 0.315996069 + 0.078125

Combine like terms: -0.078125 + 0.078125 = 0.000000
0.000000 + n = 0.315996069 + 0.078125
n = 0.315996069 + 0.078125

Combine like terms: 0.315996069 + 0.078125 = 0.394121069
n = 0.394121069

Simplifying
n = 0.394121069

Subproblem 2
n + -0.078125 = -0.315996069

Simplifying
n + -0.078125 = -0.315996069

Reorder the terms:
-0.078125 + n = -0.315996069

Solving
-0.078125 + n = -0.315996069

Solving for variable 'n'.

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

Add '0.078125' to each side of the equation.
-0.078125 + 0.078125 + n = -0.315996069 + 0.078125

Combine like terms: -0.078125 + 0.078125 = 0.000000
0.000000 + n = -0.315996069 + 0.078125
n = -0.315996069 + 0.078125

Combine like terms: -0.315996069 + 0.078125 = -0.237871069
n = -0.237871069

Simplifying
n = -0.237871069

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.394121069, -0.237871069}
Solution
n = {0.394121069, -0.237871069}