4x(6-8x)+6=8

Solution for 4x(6-8x)+6=8 equation:

Simplifying
4x(6 + -8x) + 6 = 8
(6 * 4x + -8x * 4x) + 6 = 8
(24x + -32x2) + 6 = 8

Reorder the terms:
6 + 24x + -32x2 = 8

Solving
6 + 24x + -32x2 = 8

Solving for variable 'x'.

Reorder the terms:
6 + -8 + 24x + -32x2 = 8 + -8

Combine like terms: 6 + -8 = -2
-2 + 24x + -32x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-2 + 24x + -32x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 12x + -16x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 12x + -16x2)' equal to zero and attempt to solve:

Simplifying
-1 + 12x + -16x2 = 0

Solving
-1 + 12x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.0625 + -0.75x + x2 = 0

Move the constant term to the right:

Add '-0.0625' to each side of the equation.
0.0625 + -0.75x + -0.0625 + x2 = 0 + -0.0625

Reorder the terms:
0.0625 + -0.0625 + -0.75x + x2 = 0 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + -0.75x + x2 = 0 + -0.0625
-0.75x + x2 = 0 + -0.0625

Combine like terms: 0 + -0.0625 = -0.0625
-0.75x + x2 = -0.0625

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = -0.0625 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = -0.0625 + 0.140625

Combine like terms: -0.0625 + 0.140625 = 0.078125
0.140625 + -0.75x + x2 = 0.078125

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.078125

Calculate the square root of the right side: 0.279508497

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.279508497 and -0.279508497.

Subproblem 1
x + -0.375 = 0.279508497

Simplifying
x + -0.375 = 0.279508497

Reorder the terms:
-0.375 + x = 0.279508497

Solving
-0.375 + x = 0.279508497

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 0.279508497 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 0.279508497 + 0.375
x = 0.279508497 + 0.375

Combine like terms: 0.279508497 + 0.375 = 0.654508497
x = 0.654508497

Simplifying
x = 0.654508497

Subproblem 2
x + -0.375 = -0.279508497

Simplifying
x + -0.375 = -0.279508497

Reorder the terms:
-0.375 + x = -0.279508497

Solving
-0.375 + x = -0.279508497

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -0.279508497 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -0.279508497 + 0.375
x = -0.279508497 + 0.375

Combine like terms: -0.279508497 + 0.375 = 0.095491503
x = 0.095491503

Simplifying
x = 0.095491503

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.654508497, 0.095491503}
Solution
x = {0.654508497, 0.095491503}