(1+x)(y+1)=1+xy

Solution for (1+x)(y+1)=1+xy equation:

Simplifying
(1 + x)(y + 1) = 1 + xy

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

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

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

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

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

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

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

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

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

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

Solving
1x + 1y = 0

Solving for variable 'x'.

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

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

Combine like terms: 1y + -1y = 0
1x + 0 = 0 + -1y
1x = 0 + -1y
Remove the zero:
1x = -1y

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

Simplifying
x = -1y