(x-1)(4x-4)=(x+1)(2x-2)

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Solution for (x-1)(4x-4)=(x+1)(2x-2) equation: 


Simplifying
(x + -1)(4x + -4) = (x + 1)(2x + -2)

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

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

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

Combine like terms: -4x + -4x = -8x
(4 + -8x + 4x2) = (x + 1)(2x + -2)

Reorder the terms:
4 + -8x + 4x2 = (1 + x)(2x + -2)

Reorder the terms:
4 + -8x + 4x2 = (1 + x)(-2 + 2x)

Multiply (1 + x) * (-2 + 2x)
4 + -8x + 4x2 = (1(-2 + 2x) + x(-2 + 2x))
4 + -8x + 4x2 = ((-2 * 1 + 2x * 1) + x(-2 + 2x))
4 + -8x + 4x2 = ((-2 + 2x) + x(-2 + 2x))
4 + -8x + 4x2 = (-2 + 2x + (-2 * x + 2x * x))
4 + -8x + 4x2 = (-2 + 2x + (-2x + 2x2))

Combine like terms: 2x + -2x = 0
4 + -8x + 4x2 = (-2 + 0 + 2x2)
4 + -8x + 4x2 = (-2 + 2x2)

Solving
4 + -8x + 4x2 = -2 + 2x2

Solving for variable 'x'.

Reorder the terms:
4 + 2 + -8x + 4x2 + -2x2 = -2 + 2x2 + 2 + -2x2

Combine like terms: 4 + 2 = 6
6 + -8x + 4x2 + -2x2 = -2 + 2x2 + 2 + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
6 + -8x + 2x2 = -2 + 2x2 + 2 + -2x2

Reorder the terms:
6 + -8x + 2x2 = -2 + 2 + 2x2 + -2x2

Combine like terms: -2 + 2 = 0
6 + -8x + 2x2 = 0 + 2x2 + -2x2
6 + -8x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -4x + x2) = 0

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

Ignore the factor 2.

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 '(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
Solution
x = {1, 3}

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