x(3x+2)(x-6)(x+4)=0

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Solution for x(3x+2)(x-6)(x+4)=0 equation: 


Simplifying
x(3x + 2)(x + -6)(x + 4) = 0

Reorder the terms:
x(2 + 3x)(x + -6)(x + 4) = 0

Reorder the terms:
x(2 + 3x)(-6 + x)(x + 4) = 0

Reorder the terms:
x(2 + 3x)(-6 + x)(4 + x) = 0

Multiply (2 + 3x) * (-6 + x)
x(2(-6 + x) + 3x * (-6 + x))(4 + x) = 0
x((-6 * 2 + x * 2) + 3x * (-6 + x))(4 + x) = 0
x((-12 + 2x) + 3x * (-6 + x))(4 + x) = 0
x(-12 + 2x + (-6 * 3x + x * 3x))(4 + x) = 0
x(-12 + 2x + (-18x + 3x2))(4 + x) = 0

Combine like terms: 2x + -18x = -16x
x(-12 + -16x + 3x2)(4 + x) = 0

Multiply (-12 + -16x + 3x2) * (4 + x)
x(-12(4 + x) + -16x * (4 + x) + 3x2 * (4 + x)) = 0
x((4 * -12 + x * -12) + -16x * (4 + x) + 3x2 * (4 + x)) = 0
x((-48 + -12x) + -16x * (4 + x) + 3x2 * (4 + x)) = 0
x(-48 + -12x + (4 * -16x + x * -16x) + 3x2 * (4 + x)) = 0
x(-48 + -12x + (-64x + -16x2) + 3x2 * (4 + x)) = 0
x(-48 + -12x + -64x + -16x2 + (4 * 3x2 + x * 3x2)) = 0
x(-48 + -12x + -64x + -16x2 + (12x2 + 3x3)) = 0

Combine like terms: -12x + -64x = -76x
x(-48 + -76x + -16x2 + 12x2 + 3x3) = 0

Combine like terms: -16x2 + 12x2 = -4x2
x(-48 + -76x + -4x2 + 3x3) = 0
(-48 * x + -76x * x + -4x2 * x + 3x3 * x) = 0
(-48x + -76x2 + -4x3 + 3x4) = 0

Solving
-48x + -76x2 + -4x3 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-48 + -76x + -4x2 + 3x3) = 0


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 '(-48 + -76x + -4x2 + 3x3)' equal to zero and attempt to solve:

Simplifying
-48 + -76x + -4x2 + 3x3 = 0

Solving
-48 + -76x + -4x2 + 3x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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