(2x-2)x(3x-6)-(3x-6)-(3x-27)2x=0

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Solution for (2x-2)x(3x-6)-(3x-6)-(3x-27)2x=0 equation: 


Simplifying
(2x + -2) * x(3x + -6) + -1(3x + -6) + -1(3x + -27) * 2x = 0

Reorder the terms:
(-2 + 2x) * x(3x + -6) + -1(3x + -6) + -1(3x + -27) * 2x = 0

Reorder the terms:
(-2 + 2x) * x(-6 + 3x) + -1(3x + -6) + -1(3x + -27) * 2x = 0

Reorder the terms for easier multiplication:
x(-2 + 2x)(-6 + 3x) + -1(3x + -6) + -1(3x + -27) * 2x = 0

Multiply (-2 + 2x) * (-6 + 3x)
x(-2(-6 + 3x) + 2x * (-6 + 3x)) + -1(3x + -6) + -1(3x + -27) * 2x = 0
x((-6 * -2 + 3x * -2) + 2x * (-6 + 3x)) + -1(3x + -6) + -1(3x + -27) * 2x = 0
x((12 + -6x) + 2x * (-6 + 3x)) + -1(3x + -6) + -1(3x + -27) * 2x = 0
x(12 + -6x + (-6 * 2x + 3x * 2x)) + -1(3x + -6) + -1(3x + -27) * 2x = 0
x(12 + -6x + (-12x + 6x2)) + -1(3x + -6) + -1(3x + -27) * 2x = 0

Combine like terms: -6x + -12x = -18x
x(12 + -18x + 6x2) + -1(3x + -6) + -1(3x + -27) * 2x = 0
(12 * x + -18x * x + 6x2 * x) + -1(3x + -6) + -1(3x + -27) * 2x = 0
(12x + -18x2 + 6x3) + -1(3x + -6) + -1(3x + -27) * 2x = 0

Reorder the terms:
12x + -18x2 + 6x3 + -1(-6 + 3x) + -1(3x + -27) * 2x = 0
12x + -18x2 + 6x3 + (-6 * -1 + 3x * -1) + -1(3x + -27) * 2x = 0
12x + -18x2 + 6x3 + (6 + -3x) + -1(3x + -27) * 2x = 0

Reorder the terms:
12x + -18x2 + 6x3 + 6 + -3x + -1(-27 + 3x) * 2x = 0

Reorder the terms for easier multiplication:
12x + -18x2 + 6x3 + 6 + -3x + -1 * 2x(-27 + 3x) = 0

Multiply -1 * 2
12x + -18x2 + 6x3 + 6 + -3x + -2x(-27 + 3x) = 0
12x + -18x2 + 6x3 + 6 + -3x + (-27 * -2x + 3x * -2x) = 0
12x + -18x2 + 6x3 + 6 + -3x + (54x + -6x2) = 0

Reorder the terms:
6 + 12x + -3x + 54x + -18x2 + -6x2 + 6x3 = 0

Combine like terms: 12x + -3x = 9x
6 + 9x + 54x + -18x2 + -6x2 + 6x3 = 0

Combine like terms: 9x + 54x = 63x
6 + 63x + -18x2 + -6x2 + 6x3 = 0

Combine like terms: -18x2 + -6x2 = -24x2
6 + 63x + -24x2 + 6x3 = 0

Solving
6 + 63x + -24x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 21x + -8x2 + 2x3) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + 21x + -8x2 + 2x3)' equal to zero and attempt to solve:

Simplifying
2 + 21x + -8x2 + 2x3 = 0

Solving
2 + 21x + -8x2 + 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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