a-b(y+1)=y-1(a+b)

Solution for a-b(y+1)=y-1(a+b) equation:

Simplifying
a + -1b(y + 1) = y + -1(a + b)

Reorder the terms:
a + -1b(1 + y) = y + -1(a + b)
a + (1 * -1b + y * -1b) = y + -1(a + b)
a + (-1b + -1by) = y + -1(a + b)
a + -1b + -1by = y + (a * -1 + b * -1)
a + -1b + -1by = y + (-1a + -1b)

Reorder the terms:
a + -1b + -1by = -1a + -1b + y

Add 'b' to each side of the equation.
a + -1b + b + -1by = -1a + -1b + b + y

Combine like terms: -1b + b = 0
a + 0 + -1by = -1a + -1b + b + y
a + -1by = -1a + -1b + b + y

Combine like terms: -1b + b = 0
a + -1by = -1a + 0 + y
a + -1by = -1a + y

Solving
a + -1by = -1a + y

Solving for variable 'a'.

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

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

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

Combine like terms: -1a + a = 0
2a + -1by = 0 + y
2a + -1by = y

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

Combine like terms: -1by + by = 0
2a + 0 = by + y
2a = by + y

Divide each side by '2'.
a = 0.5by + 0.5y

Simplifying
a = 0.5by + 0.5y