8(16x^2-1)+2=-8(4x-1)

Solution for 8(16x^2-1)+2=-8(4x-1) equation:

Simplifying
8(16x2 + -1) + 2 = -8(4x + -1)

Reorder the terms:
8(-1 + 16x2) + 2 = -8(4x + -1)
(-1 * 8 + 16x2 * 8) + 2 = -8(4x + -1)
(-8 + 128x2) + 2 = -8(4x + -1)

Reorder the terms:
-8 + 2 + 128x2 = -8(4x + -1)

Combine like terms: -8 + 2 = -6
-6 + 128x2 = -8(4x + -1)

Reorder the terms:
-6 + 128x2 = -8(-1 + 4x)
-6 + 128x2 = (-1 * -8 + 4x * -8)
-6 + 128x2 = (8 + -32x)

Solving
-6 + 128x2 = 8 + -32x

Solving for variable 'x'.

Reorder the terms:
-6 + -8 + 32x + 128x2 = 8 + -32x + -8 + 32x

Combine like terms: -6 + -8 = -14
-14 + 32x + 128x2 = 8 + -32x + -8 + 32x

Reorder the terms:
-14 + 32x + 128x2 = 8 + -8 + -32x + 32x

Combine like terms: 8 + -8 = 0
-14 + 32x + 128x2 = 0 + -32x + 32x
-14 + 32x + 128x2 = -32x + 32x

Combine like terms: -32x + 32x = 0
-14 + 32x + 128x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 16x + 64x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + 16x + 64x2)' equal to zero and attempt to solve:

Simplifying
-7 + 16x + 64x2 = 0

Solving
-7 + 16x + 64x2 = 0

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

Divide each side by '64'.
-0.109375 + 0.25x + x2 = 0

Move the constant term to the right:

Add '0.109375' to each side of the equation.
-0.109375 + 0.25x + 0.109375 + x2 = 0 + 0.109375

Reorder the terms:
-0.109375 + 0.109375 + 0.25x + x2 = 0 + 0.109375

Combine like terms: -0.109375 + 0.109375 = 0.000000
0.000000 + 0.25x + x2 = 0 + 0.109375
0.25x + x2 = 0 + 0.109375

Combine like terms: 0 + 0.109375 = 0.109375
0.25x + x2 = 0.109375

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 0.109375 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 0.109375 + 0.015625

Combine like terms: 0.109375 + 0.015625 = 0.125
0.015625 + 0.25x + x2 = 0.125

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(x + 0.125) equal to 0.353553391 and -0.353553391.

Subproblem 1
x + 0.125 = 0.353553391

Simplifying
x + 0.125 = 0.353553391

Reorder the terms:
0.125 + x = 0.353553391

Solving
0.125 + x = 0.353553391

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = 0.353553391 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 0.353553391 + -0.125
x = 0.353553391 + -0.125

Combine like terms: 0.353553391 + -0.125 = 0.228553391
x = 0.228553391

Simplifying
x = 0.228553391

Subproblem 2
x + 0.125 = -0.353553391

Simplifying
x + 0.125 = -0.353553391

Reorder the terms:
0.125 + x = -0.353553391

Solving
0.125 + x = -0.353553391

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = -0.353553391 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -0.353553391 + -0.125
x = -0.353553391 + -0.125

Combine like terms: -0.353553391 + -0.125 = -0.478553391
x = -0.478553391

Simplifying
x = -0.478553391

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.228553391, -0.478553391}
Solution
x = {0.228553391, -0.478553391}