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

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


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

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

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

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

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

Multiply (3 + 2x) * (-3 + 2x)
3x(3(-3 + 2x) + 2x * (-3 + 2x)) = 0
3x((-3 * 3 + 2x * 3) + 2x * (-3 + 2x)) = 0
3x((-9 + 6x) + 2x * (-3 + 2x)) = 0
3x(-9 + 6x + (-3 * 2x + 2x * 2x)) = 0
3x(-9 + 6x + (-6x + 4x2)) = 0

Combine like terms: 6x + -6x = 0
3x(-9 + 0 + 4x2) = 0
3x(-9 + 4x2) = 0
(-9 * 3x + 4x2 * 3x) = 0
(-27x + 12x3) = 0

Solving
-27x + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-9 + 4x2) = 0

Factor a difference between two squares.
3x((3 + 2x)(-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 '(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

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, -1.5, 1.5}

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