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

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


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

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

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

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

Combine like terms: -4x + 2x = -2x
3x(-8 + -2x + x2) = 0
(-8 * 3x + -2x * 3x + x2 * 3x) = 0
(-24x + -6x2 + 3x3) = 0

Solving
-24x + -6x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-8 + -2x + x2) = 0

Factor a trinomial.
3x((-2 + -1x)(4 + -1x)) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, -2, 4}

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