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

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


Simplifying
(x + -2)(3x + -6) = 27

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

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

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

Combine like terms: -6x + -6x = -12x
(12 + -12x + 3x2) = 27

Solving
12 + -12x + 3x2 = 27

Solving for variable 'x'.

Reorder the terms:
12 + -27 + -12x + 3x2 = 27 + -27

Combine like terms: 12 + -27 = -15
-15 + -12x + 3x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-15 + -12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -4x + x2) = 0

Factor a trinomial.
3((-1 + -1x)(5 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1

Combine like terms: 0 + 1 = 1
-1x = 1

Divide each side by '-1'.
x = -1

Simplifying
x = -1

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1, 5}

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