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

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


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

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

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

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

Combine like terms: -2x + 6x = 4x
(-12 + 4x + x2) = 3(x + -2)

Reorder the terms:
-12 + 4x + x2 = 3(-2 + x)
-12 + 4x + x2 = (-2 * 3 + x * 3)
-12 + 4x + x2 = (-6 + 3x)

Solving
-12 + 4x + x2 = -6 + 3x

Solving for variable 'x'.

Reorder the terms:
-12 + 6 + 4x + -3x + x2 = -6 + 3x + 6 + -3x

Combine like terms: -12 + 6 = -6
-6 + 4x + -3x + x2 = -6 + 3x + 6 + -3x

Combine like terms: 4x + -3x = 1x
-6 + 1x + x2 = -6 + 3x + 6 + -3x

Reorder the terms:
-6 + 1x + x2 = -6 + 6 + 3x + -3x

Combine like terms: -6 + 6 = 0
-6 + 1x + x2 = 0 + 3x + -3x
-6 + 1x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-6 + 1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}

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