3x(2x-1)(3x+2)=0

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Solution for 3x(2x-1)(3x+2)=0 equation: 


Simplifying
3x(2x + -1)(3x + 2) = 0

Reorder the terms:
3x(-1 + 2x)(3x + 2) = 0

Reorder the terms:
3x(-1 + 2x)(2 + 3x) = 0

Multiply (-1 + 2x) * (2 + 3x)
3x(-1(2 + 3x) + 2x * (2 + 3x)) = 0
3x((2 * -1 + 3x * -1) + 2x * (2 + 3x)) = 0
3x((-2 + -3x) + 2x * (2 + 3x)) = 0
3x(-2 + -3x + (2 * 2x + 3x * 2x)) = 0
3x(-2 + -3x + (4x + 6x2)) = 0

Combine like terms: -3x + 4x = 1x
3x(-2 + 1x + 6x2) = 0
(-2 * 3x + 1x * 3x + 6x2 * 3x) = 0
(-6x + 3x2 + 18x3) = 0

Solving
-6x + 3x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-2 + x + 6x2) = 0

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

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, -0.6666666667, 0.5}

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