0=8x^2-8x+6

Solution for 0=8x^2-8x+6 equation:

Simplifying
0 = 8x2 + -8x + 6

Reorder the terms:
0 = 6 + -8x + 8x2

Solving
0 = 6 + -8x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + 8x + -8x2 = 6 + -8x + 8x2 + -6 + 8x + -8x2

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

Combine like terms: 6 + -6 = 0
-6 + 8x + -8x2 = 0 + -8x + 8x + 8x2 + -8x2
-6 + 8x + -8x2 = -8x + 8x + 8x2 + -8x2

Combine like terms: -8x + 8x = 0
-6 + 8x + -8x2 = 0 + 8x2 + -8x2
-6 + 8x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-6 + 8x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 4x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 4x + -4x2)' equal to zero and attempt to solve:

Simplifying
-3 + 4x + -4x2 = 0

Solving
-3 + 4x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.75 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -1x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -1x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -1x + x2 = 0 + -0.75
-1x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-1x + x2 = -0.75

The x term is -1x.  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.
-1x + 0.25 + x2 = -0.75 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.75 + 0.25

Combine like terms: -0.75 + 0.25 = -0.5
0.25 + -1x + x2 = -0.5

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

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.