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

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


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

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

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

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

Multiply (3 + 2x) * (4 + x)
(3(4 + x) + 2x * (4 + x))(-6 + 3x) = 0
((4 * 3 + x * 3) + 2x * (4 + x))(-6 + 3x) = 0
((12 + 3x) + 2x * (4 + x))(-6 + 3x) = 0
(12 + 3x + (4 * 2x + x * 2x))(-6 + 3x) = 0
(12 + 3x + (8x + 2x2))(-6 + 3x) = 0

Combine like terms: 3x + 8x = 11x
(12 + 11x + 2x2)(-6 + 3x) = 0

Multiply (12 + 11x + 2x2) * (-6 + 3x)
(12(-6 + 3x) + 11x * (-6 + 3x) + 2x2 * (-6 + 3x)) = 0
((-6 * 12 + 3x * 12) + 11x * (-6 + 3x) + 2x2 * (-6 + 3x)) = 0
((-72 + 36x) + 11x * (-6 + 3x) + 2x2 * (-6 + 3x)) = 0
(-72 + 36x + (-6 * 11x + 3x * 11x) + 2x2 * (-6 + 3x)) = 0
(-72 + 36x + (-66x + 33x2) + 2x2 * (-6 + 3x)) = 0
(-72 + 36x + -66x + 33x2 + (-6 * 2x2 + 3x * 2x2)) = 0
(-72 + 36x + -66x + 33x2 + (-12x2 + 6x3)) = 0

Combine like terms: 36x + -66x = -30x
(-72 + -30x + 33x2 + -12x2 + 6x3) = 0

Combine like terms: 33x2 + -12x2 = 21x2
(-72 + -30x + 21x2 + 6x3) = 0

Solving
-72 + -30x + 21x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -10x + 7x2 + 2x3) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-24 + -10x + 7x2 + 2x3)' equal to zero and attempt to solve:

Simplifying
-24 + -10x + 7x2 + 2x3 = 0

Solving
-24 + -10x + 7x2 + 2x3 = 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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