0=6x(3x-2)(3x+2)

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Solution for 0=6x(3x-2)(3x+2) equation: 


Simplifying
0 = 6x(3x + -2)(3x + 2)

Reorder the terms:
0 = 6x(-2 + 3x)(3x + 2)

Reorder the terms:
0 = 6x(-2 + 3x)(2 + 3x)

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

Combine like terms: -6x + 6x = 0
0 = 6x(-4 + 0 + 9x2)
0 = 6x(-4 + 9x2)
0 = (-4 * 6x + 9x2 * 6x)
0 = (-24x + 54x3)

Solving
0 = -24x + 54x3

Solving for variable 'x'.
Remove the zero:
24x + -54x3 = -24x + 54x3 + 24x + -54x3

Reorder the terms:
24x + -54x3 = -24x + 24x + 54x3 + -54x3

Combine like terms: -24x + 24x = 0
24x + -54x3 = 0 + 54x3 + -54x3
24x + -54x3 = 54x3 + -54x3

Combine like terms: 54x3 + -54x3 = 0
24x + -54x3 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(4 + -9x2) = 0

Factor a difference between two squares.
6x((2 + 3x)(2 + -3x)) = 0

Ignore the factor 6.

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 '(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
Solution
x = {0, -0.6666666667, 0.6666666667}

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