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

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


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

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

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

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

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

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

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

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

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

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

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

Combine like terms: -18x + -3x = -21x
18 + -21x + 54x + 6x2 + -6x2 = 0

Combine like terms: -21x + 54x = 33x
18 + 33x + 6x2 + -6x2 = 0

Combine like terms: 6x2 + -6x2 = 0
18 + 33x + 0 = 0
18 + 33x = 0

Solving
18 + 33x = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-18' to each side of the equation.
18 + -18 + 33x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 33x = 0 + -18
33x = 0 + -18

Combine like terms: 0 + -18 = -18
33x = -18

Divide each side by '33'.
x = -0.5454545455

Simplifying
x = -0.5454545455

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