5-(2x-1)(x-1)=(1-x)(2x-2)

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Solution for 5-(2x-1)(x-1)=(1-x)(2x-2) equation: 


Simplifying
5 + -1(2x + -1)(x + -1) = (1 + -1x)(2x + -2)

Reorder the terms:
5 + -1(-1 + 2x)(x + -1) = (1 + -1x)(2x + -2)

Reorder the terms:
5 + -1(-1 + 2x)(-1 + x) = (1 + -1x)(2x + -2)

Multiply (-1 + 2x) * (-1 + x)
5 + -1(-1(-1 + x) + 2x * (-1 + x)) = (1 + -1x)(2x + -2)
5 + -1((-1 * -1 + x * -1) + 2x * (-1 + x)) = (1 + -1x)(2x + -2)
5 + -1((1 + -1x) + 2x * (-1 + x)) = (1 + -1x)(2x + -2)
5 + -1(1 + -1x + (-1 * 2x + x * 2x)) = (1 + -1x)(2x + -2)
5 + -1(1 + -1x + (-2x + 2x2)) = (1 + -1x)(2x + -2)

Combine like terms: -1x + -2x = -3x
5 + -1(1 + -3x + 2x2) = (1 + -1x)(2x + -2)
5 + (1 * -1 + -3x * -1 + 2x2 * -1) = (1 + -1x)(2x + -2)
5 + (-1 + 3x + -2x2) = (1 + -1x)(2x + -2)

Combine like terms: 5 + -1 = 4
4 + 3x + -2x2 = (1 + -1x)(2x + -2)

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

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

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

Add '2x2' to each side of the equation.
4 + 3x + -2x2 + 2x2 = -2 + 4x + -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
4 + 3x + 0 = -2 + 4x + -2x2 + 2x2
4 + 3x = -2 + 4x + -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
4 + 3x = -2 + 4x + 0
4 + 3x = -2 + 4x

Solving
4 + 3x = -2 + 4x

Solving for variable 'x'.

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

Add '-4x' to each side of the equation.
4 + 3x + -4x = -2 + 4x + -4x

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

Combine like terms: 4x + -4x = 0
4 + -1x = -2 + 0
4 + -1x = -2

Add '-4' to each side of the equation.
4 + -4 + -1x = -2 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = -2 + -4
-1x = -2 + -4

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6

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