x(x-3)(3x+12)(2x-4)=0

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Solution for x(x-3)(3x+12)(2x-4)=0 equation:


Simplifying
x(x + -3)(3x + 12)(2x + -4) = 0

Reorder the terms:
x(-3 + x)(3x + 12)(2x + -4) = 0

Reorder the terms:
x(-3 + x)(12 + 3x)(2x + -4) = 0

Reorder the terms:
x(-3 + x)(12 + 3x)(-4 + 2x) = 0

Multiply (-3 + x) * (12 + 3x)
x(-3(12 + 3x) + x(12 + 3x))(-4 + 2x) = 0
x((12 * -3 + 3x * -3) + x(12 + 3x))(-4 + 2x) = 0
x((-36 + -9x) + x(12 + 3x))(-4 + 2x) = 0
x(-36 + -9x + (12 * x + 3x * x))(-4 + 2x) = 0
x(-36 + -9x + (12x + 3x2))(-4 + 2x) = 0

Combine like terms: -9x + 12x = 3x
x(-36 + 3x + 3x2)(-4 + 2x) = 0

Multiply (-36 + 3x + 3x2) * (-4 + 2x)
x(-36(-4 + 2x) + 3x * (-4 + 2x) + 3x2 * (-4 + 2x)) = 0
x((-4 * -36 + 2x * -36) + 3x * (-4 + 2x) + 3x2 * (-4 + 2x)) = 0
x((144 + -72x) + 3x * (-4 + 2x) + 3x2 * (-4 + 2x)) = 0
x(144 + -72x + (-4 * 3x + 2x * 3x) + 3x2 * (-4 + 2x)) = 0
x(144 + -72x + (-12x + 6x2) + 3x2 * (-4 + 2x)) = 0
x(144 + -72x + -12x + 6x2 + (-4 * 3x2 + 2x * 3x2)) = 0
x(144 + -72x + -12x + 6x2 + (-12x2 + 6x3)) = 0

Combine like terms: -72x + -12x = -84x
x(144 + -84x + 6x2 + -12x2 + 6x3) = 0

Combine like terms: 6x2 + -12x2 = -6x2
x(144 + -84x + -6x2 + 6x3) = 0
(144 * x + -84x * x + -6x2 * x + 6x3 * x) = 0
(144x + -84x2 + -6x3 + 6x4) = 0

Solving
144x + -84x2 + -6x3 + 6x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(24 + -14x + -1x2 + x3) = 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 '(24 + -14x + -1x2 + x3)' equal to zero and attempt to solve:

Simplifying
24 + -14x + -1x2 + x3 = 0

Solving
24 + -14x + -1x2 + x3 = 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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