-3x(x^2-4x+6)=

Solution for -3x(x^2-4x+6)= equation:

Simplifying
-3x(x2 + -4x + 6) = 0

Reorder the terms:
-3x(6 + -4x + x2) = 0
(6 * -3x + -4x * -3x + x2 * -3x) = 0
(-18x + 12x2 + -3x3) = 0

Solving
-18x + 12x2 + -3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-6 + 4x + -1x2) = 0

Ignore the factor 3.
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 + 4x + -1x2)' equal to zero and attempt to solve:

Simplifying
-6 + 4x + -1x2 = 0

Solving
-6 + 4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
6 + -4x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -4x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -4x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -4x + x2 = 0 + -6
-4x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-4x + x2 = -6

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -6 + 4

Reorder the terms:
4 + -4x + x2 = -6 + 4

Combine like terms: -6 + 4 = -2
4 + -4x + x2 = -2

Factor a perfect square on the left side:
(x + -2)(x + -2) = -2

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}