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

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


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

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

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

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

Combine like terms: 6x + -3x = 3x
2x(-2 + 3x + 9x2) = 0
(-2 * 2x + 3x * 2x + 9x2 * 2x) = 0
(-4x + 6x2 + 18x3) = 0

Solving
-4x + 6x2 + 18x3 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.

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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