(Y-3)-(y-2)=5

Solution for (Y-3)-(y-2)=5 equation:

Simplifying
(Y + -3) + -1(y + -2) = 5

Reorder the terms:
(-3 + Y) + -1(y + -2) = 5

Remove parenthesis around (-3 + Y)
-3 + Y + -1(y + -2) = 5

Reorder the terms:
-3 + Y + -1(-2 + y) = 5
-3 + Y + (-2 * -1 + y * -1) = 5
-3 + Y + (2 + -1y) = 5

Reorder the terms:
-3 + 2 + Y + -1y = 5

Combine like terms: -3 + 2 = -1
-1 + Y + -1y = 5

Solving
-1 + Y + -1y = 5

Solving for variable 'Y'.

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

Add '1' to each side of the equation.
-1 + Y + 1 + -1y = 5 + 1

Reorder the terms:
-1 + 1 + Y + -1y = 5 + 1

Combine like terms: -1 + 1 = 0
0 + Y + -1y = 5 + 1
Y + -1y = 5 + 1

Combine like terms: 5 + 1 = 6
Y + -1y = 6

Add 'y' to each side of the equation.
Y + -1y + y = 6 + y

Combine like terms: -1y + y = 0
Y + 0 = 6 + y
Y = 6 + y

Simplifying
Y = 6 + y