(x-3)-(y-3)=2

Solution for (x-3)-(y-3)=2 equation:

Simplifying
(x + -3) + -1(y + -3) = 2

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

Remove parenthesis around (-3 + x)
-3 + x + -1(y + -3) = 2

Reorder the terms:
-3 + x + -1(-3 + y) = 2
-3 + x + (-3 * -1 + y * -1) = 2
-3 + x + (3 + -1y) = 2

Reorder the terms:
-3 + 3 + x + -1y = 2

Combine like terms: -3 + 3 = 0
0 + x + -1y = 2
x + -1y = 2

Solving
x + -1y = 2

Solving for variable 'x'.

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

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

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

Simplifying
x = 2 + y