(2x-2)(x-2)=(x-1)(x+3)

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Solution for (2x-2)(x-2)=(x-1)(x+3) equation: 


Simplifying
(2x + -2)(x + -2) = (x + -1)(x + 3)

Reorder the terms:
(-2 + 2x)(x + -2) = (x + -1)(x + 3)

Reorder the terms:
(-2 + 2x)(-2 + x) = (x + -1)(x + 3)

Multiply (-2 + 2x) * (-2 + x)
(-2(-2 + x) + 2x * (-2 + x)) = (x + -1)(x + 3)
((-2 * -2 + x * -2) + 2x * (-2 + x)) = (x + -1)(x + 3)
((4 + -2x) + 2x * (-2 + x)) = (x + -1)(x + 3)
(4 + -2x + (-2 * 2x + x * 2x)) = (x + -1)(x + 3)
(4 + -2x + (-4x + 2x2)) = (x + -1)(x + 3)

Combine like terms: -2x + -4x = -6x
(4 + -6x + 2x2) = (x + -1)(x + 3)

Reorder the terms:
4 + -6x + 2x2 = (-1 + x)(x + 3)

Reorder the terms:
4 + -6x + 2x2 = (-1 + x)(3 + x)

Multiply (-1 + x) * (3 + x)
4 + -6x + 2x2 = (-1(3 + x) + x(3 + x))
4 + -6x + 2x2 = ((3 * -1 + x * -1) + x(3 + x))
4 + -6x + 2x2 = ((-3 + -1x) + x(3 + x))
4 + -6x + 2x2 = (-3 + -1x + (3 * x + x * x))
4 + -6x + 2x2 = (-3 + -1x + (3x + x2))

Combine like terms: -1x + 3x = 2x
4 + -6x + 2x2 = (-3 + 2x + x2)

Solving
4 + -6x + 2x2 = -3 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
4 + 3 + -6x + -2x + 2x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Combine like terms: 4 + 3 = 7
7 + -6x + -2x + 2x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Combine like terms: -6x + -2x = -8x
7 + -8x + 2x2 + -1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
7 + -8x + 1x2 = -3 + 2x + x2 + 3 + -2x + -1x2

Reorder the terms:
7 + -8x + 1x2 = -3 + 3 + 2x + -2x + x2 + -1x2

Combine like terms: -3 + 3 = 0
7 + -8x + 1x2 = 0 + 2x + -2x + x2 + -1x2
7 + -8x + 1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
7 + -8x + 1x2 = 0 + x2 + -1x2
7 + -8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + -8x + 1x2 = 0

Factor a trinomial.
(1 + -1x)(7 + -1x) = 0


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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1, 7}

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