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

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


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

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

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

Multiply (-1 + 3x) * (2 + 3x)
x(-1(2 + 3x) + 3x * (2 + 3x)) = 0
x((2 * -1 + 3x * -1) + 3x * (2 + 3x)) = 0
x((-2 + -3x) + 3x * (2 + 3x)) = 0
x(-2 + -3x + (2 * 3x + 3x * 3x)) = 0
x(-2 + -3x + (6x + 9x2)) = 0

Combine like terms: -3x + 6x = 3x
x(-2 + 3x + 9x2) = 0
(-2 * x + 3x * x + 9x2 * x) = 0
(-2x + 3x2 + 9x3) = 0

Solving
-2x + 3x2 + 9x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2 + 3x + 9x2) = 0

Factor a trinomial.
x((-2 + -3x)(1 + -3x)) = 0


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 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, -0.6666666667, 0.3333333333}

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