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

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

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

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

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

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

Multiply (-3 + 2x) * (3 + 3x)
x(-3(3 + 3x) + 2x * (3 + 3x)) = 0
x((3 * -3 + 3x * -3) + 2x * (3 + 3x)) = 0
x((-9 + -9x) + 2x * (3 + 3x)) = 0
x(-9 + -9x + (3 * 2x + 3x * 2x)) = 0
x(-9 + -9x + (6x + 6x2)) = 0

Combine like terms: -9x + 6x = -3x
x(-9 + -3x + 6x2) = 0
(-9 * x + -3x * x + 6x2 * x) = 0
(-9x + -3x2 + 6x3) = 0

Solving
-9x + -3x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-3 + -1x + 2x2) = 0

Factor a trinomial.
3x((-1 + -1x)(3 + -2x)) = 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 '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1
Subproblem 3
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, -1, 1.5}