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

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

Simplifying
4x3 + -2x2 + 12x = 0

Reorder the terms:
12x + -2x2 + 4x3 = 0

Solving
12x + -2x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(6 + -1x + 2x2) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(6 + -1x + 2x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x + 2x2 = 0

Solving
6 + -1x + 2x2 = 0

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

Divide each side by '2'.
3 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -0.5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -0.5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -0.5x + x2 = 0 + -3
-0.5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-0.5x + x2 = -3

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 = -3 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -3 + 0.0625

Combine like terms: -3 + 0.0625 = -2.9375
0.0625 + -0.5x + x2 = -2.9375

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -2.9375

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}