(x-3)(2x+1)(x+2)(3x-12)=0

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Solution for (x-3)(2x+1)(x+2)(3x-12)=0 equation:


Simplifying
(x + -3)(2x + 1)(x + 2)(3x + -12) = 0

Reorder the terms:
(-3 + x)(2x + 1)(x + 2)(3x + -12) = 0

Reorder the terms:
(-3 + x)(1 + 2x)(x + 2)(3x + -12) = 0

Reorder the terms:
(-3 + x)(1 + 2x)(2 + x)(3x + -12) = 0

Reorder the terms:
(-3 + x)(1 + 2x)(2 + x)(-12 + 3x) = 0

Multiply (-3 + x) * (1 + 2x)
(-3(1 + 2x) + x(1 + 2x))(2 + x)(-12 + 3x) = 0
((1 * -3 + 2x * -3) + x(1 + 2x))(2 + x)(-12 + 3x) = 0
((-3 + -6x) + x(1 + 2x))(2 + x)(-12 + 3x) = 0
(-3 + -6x + (1 * x + 2x * x))(2 + x)(-12 + 3x) = 0
(-3 + -6x + (1x + 2x2))(2 + x)(-12 + 3x) = 0

Combine like terms: -6x + 1x = -5x
(-3 + -5x + 2x2)(2 + x)(-12 + 3x) = 0

Multiply (-3 + -5x + 2x2) * (2 + x)
(-3(2 + x) + -5x * (2 + x) + 2x2 * (2 + x))(-12 + 3x) = 0
((2 * -3 + x * -3) + -5x * (2 + x) + 2x2 * (2 + x))(-12 + 3x) = 0
((-6 + -3x) + -5x * (2 + x) + 2x2 * (2 + x))(-12 + 3x) = 0
(-6 + -3x + (2 * -5x + x * -5x) + 2x2 * (2 + x))(-12 + 3x) = 0
(-6 + -3x + (-10x + -5x2) + 2x2 * (2 + x))(-12 + 3x) = 0
(-6 + -3x + -10x + -5x2 + (2 * 2x2 + x * 2x2))(-12 + 3x) = 0
(-6 + -3x + -10x + -5x2 + (4x2 + 2x3))(-12 + 3x) = 0

Combine like terms: -3x + -10x = -13x
(-6 + -13x + -5x2 + 4x2 + 2x3)(-12 + 3x) = 0

Combine like terms: -5x2 + 4x2 = -1x2
(-6 + -13x + -1x2 + 2x3)(-12 + 3x) = 0

Multiply (-6 + -13x + -1x2 + 2x3) * (-12 + 3x)
(-6(-12 + 3x) + -13x * (-12 + 3x) + -1x2 * (-12 + 3x) + 2x3 * (-12 + 3x)) = 0
((-12 * -6 + 3x * -6) + -13x * (-12 + 3x) + -1x2 * (-12 + 3x) + 2x3 * (-12 + 3x)) = 0
((72 + -18x) + -13x * (-12 + 3x) + -1x2 * (-12 + 3x) + 2x3 * (-12 + 3x)) = 0
(72 + -18x + (-12 * -13x + 3x * -13x) + -1x2 * (-12 + 3x) + 2x3 * (-12 + 3x)) = 0
(72 + -18x + (156x + -39x2) + -1x2 * (-12 + 3x) + 2x3 * (-12 + 3x)) = 0
(72 + -18x + 156x + -39x2 + (-12 * -1x2 + 3x * -1x2) + 2x3 * (-12 + 3x)) = 0
(72 + -18x + 156x + -39x2 + (12x2 + -3x3) + 2x3 * (-12 + 3x)) = 0
(72 + -18x + 156x + -39x2 + 12x2 + -3x3 + (-12 * 2x3 + 3x * 2x3)) = 0
(72 + -18x + 156x + -39x2 + 12x2 + -3x3 + (-24x3 + 6x4)) = 0

Combine like terms: -18x + 156x = 138x
(72 + 138x + -39x2 + 12x2 + -3x3 + -24x3 + 6x4) = 0

Combine like terms: -39x2 + 12x2 = -27x2
(72 + 138x + -27x2 + -3x3 + -24x3 + 6x4) = 0

Combine like terms: -3x3 + -24x3 = -27x3
(72 + 138x + -27x2 + -27x3 + 6x4) = 0

Solving
72 + 138x + -27x2 + -27x3 + 6x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + 46x + -9x2 + -9x3 + 2x4) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(24 + 46x + -9x2 + -9x3 + 2x4)' equal to zero and attempt to solve:

Simplifying
24 + 46x + -9x2 + -9x3 + 2x4 = 0

Solving
24 + 46x + -9x2 + -9x3 + 2x4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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