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

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

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

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

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

Multiply (1 + x) * (-1 + y)
(1(-1 + y) + x(-1 + y)) = 2(y + -1x)
((-1 * 1 + y * 1) + x(-1 + y)) = 2(y + -1x)
((-1 + 1y) + x(-1 + y)) = 2(y + -1x)
(-1 + 1y + (-1 * x + y * x)) = 2(y + -1x)
(-1 + 1y + (-1x + xy)) = 2(y + -1x)

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

Reorder the terms:
-1 + -1x + xy + 1y = 2(-1x + y)
-1 + -1x + xy + 1y = (-1x * 2 + y * 2)
-1 + -1x + xy + 1y = (-2x + 2y)

Solving
-1 + -1x + xy + 1y = -2x + 2y

Solving for variable 'x'.

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

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

Reorder the terms:
-1 + -1x + 2x + xy + 1y = -2x + 2x + 2y

Combine like terms: -1x + 2x = 1x
-1 + 1x + xy + 1y = -2x + 2x + 2y

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

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

Reorder the terms:
-1 + 1 + 1x + xy + 1y = 1 + 2y

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

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

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

Combine like terms: 2y + -1y = 1y
1x + xy = 1 + 1y

Reorder the terms:
-1 + 1x + xy + -1y = 1 + 1y + -1 + -1y

Reorder the terms:
-1 + 1x + xy + -1y = 1 + -1 + 1y + -1y

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

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

The solution to this equation could not be determined.