(3x)(-2x)(x^2+3x+3)=0

Solution for (3x)(-2x)(x^2+3x+3)=0 equation:

Simplifying
(3x)(-2x)(x2 + 3x + 3) = 0

Remove parenthesis around (3x)
3x(-2x)(x2 + 3x + 3) = 0

Remove parenthesis around (-2x)
3x * -2x(x2 + 3x + 3) = 0

Reorder the terms:
3x * -2x(3 + 3x + x2) = 0

Reorder the terms for easier multiplication:
3 * -2x * x(3 + 3x + x2) = 0

Multiply 3 * -2
-6x * x(3 + 3x + x2) = 0

Multiply x * x
-6x2(3 + 3x + x2) = 0
(3 * -6x2 + 3x * -6x2 + x2 * -6x2) = 0
(-18x2 + -18x3 + -6x4) = 0

Solving
-18x2 + -18x3 + -6x4 = 0

Solving for variable 'x'.

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

Ignore the factor -6.
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 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
3 + 3x + x2 = 0

Solving
3 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -3 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -3 + 2.25

Combine like terms: -3 + 2.25 = -0.75
2.25 + 3x + x2 = -0.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -0.75

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}