6x(2x^2-2x+4)=

Solution for 6x(2x^2-2x+4)= equation:

Simplifying
6x(2x2 + -2x + 4) = 0

Reorder the terms:
6x(4 + -2x + 2x2) = 0
(4 * 6x + -2x * 6x + 2x2 * 6x) = 0
(24x + -12x2 + 12x3) = 0

Solving
24x + -12x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(2 + -1x + x2) = 0

Ignore the factor 12.
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 '(2 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x + x2 = 0

Solving
2 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -1x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x + x2 = 0 + -2
-1x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x + x2 = -2

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 = -2 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + -1x + x2 = -1.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -1.75

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}