8x^4-8x^3+6x^2=0

Solution for 8x^4-8x^3+6x^2=0 equation:

Simplifying
8x4 + -8x3 + 6x2 = 0

Reorder the terms:
6x2 + -8x3 + 8x4 = 0

Solving
6x2 + -8x3 + 8x4 = 0

Solving for variable 'x'.

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

Ignore the factor 2.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
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.
Solution
x = {0}