(x+y)-(x-y)=y

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

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

Remove parenthesis around (x + y)
x + y + -1(x + -1y) = y
x + y + (x * -1 + -1y * -1) = y
x + y + (-1x + 1y) = y

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

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

Combine like terms: y + 1y = 2y
2y = y

Solving
2y = y

Solving for variable 'y'.

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

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

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

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

Divide each side by '1'.
y = 0

Simplifying
y = 0