8x^4-4x^3+12x^2=0

Solution for 8x^4-4x^3+12x^2=0 equation:

Simplifying
8x4 + -4x3 + 12x2 = 0

Reorder the terms:
12x2 + -4x3 + 8x4 = 0

Solving
12x2 + -4x3 + 8x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(3 + -1x + 2x2) = 0

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

Simplifying
3 + -1x + 2x2 = 0

Solving
3 + -1x + 2x2 = 0

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

Divide each side by '2'.
1.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.5x + x2 = 0 + -1.5
-0.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.5x + x2 = -1.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -1.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -1.5 + 0.0625

Combine like terms: -1.5 + 0.0625 = -1.4375
0.0625 + -0.5x + x2 = -1.4375

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -1.4375

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}