3x^4-6x^3+12x^2=0

Solution for 3x^4-6x^3+12x^2=0 equation:

Simplifying
3x4 + -6x3 + 12x2 = 0

Reorder the terms:
12x2 + -6x3 + 3x4 = 0

Solving
12x2 + -6x3 + 3x4 = 0

Solving for variable 'x'.

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

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

Simplifying
4 + -2x + x2 = 0

Solving
4 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -2x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -2x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -2x + x2 = 0 + -4
-2x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-2x + x2 = -4

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -4 + 1

Reorder the terms:
1 + -2x + x2 = -4 + 1

Combine like terms: -4 + 1 = -3
1 + -2x + x2 = -3

Factor a perfect square on the left side:
(x + -1)(x + -1) = -3

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}