3x(3x-4)(3x+2)=0

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Solution for 3x(3x-4)(3x+2)=0 equation: 


Simplifying
3x(3x + -4)(3x + 2) = 0

Reorder the terms:
3x(-4 + 3x)(3x + 2) = 0

Reorder the terms:
3x(-4 + 3x)(2 + 3x) = 0

Multiply (-4 + 3x) * (2 + 3x)
3x(-4(2 + 3x) + 3x * (2 + 3x)) = 0
3x((2 * -4 + 3x * -4) + 3x * (2 + 3x)) = 0
3x((-8 + -12x) + 3x * (2 + 3x)) = 0
3x(-8 + -12x + (2 * 3x + 3x * 3x)) = 0
3x(-8 + -12x + (6x + 9x2)) = 0

Combine like terms: -12x + 6x = -6x
3x(-8 + -6x + 9x2) = 0
(-8 * 3x + -6x * 3x + 9x2 * 3x) = 0
(-24x + -18x2 + 27x3) = 0

Solving
-24x + -18x2 + 27x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-8 + -6x + 9x2) = 0

Factor a trinomial.
3x((-2 + -3x)(4 + -3x)) = 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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, -0.6666666667, 1.333333333}

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