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

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


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

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

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

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

Combine like terms: -2x + 2x = 0
3x(-4 + 0 + x2) = 0
3x(-4 + x2) = 0
(-4 * 3x + x2 * 3x) = 0
(-12x + 3x3) = 0

Solving
-12x + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4 + x2) = 0

Factor a difference between two squares.
3x((2 + x)(-2 + x)) = 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 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2

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

Simplifying
-2 + x = 0

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

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

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

Simplifying
x = 2
Solution
x = {0, -2, 2}

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