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

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

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

Reorder the terms:
b(1 + x) = b(a + x) + -1b
(1 * b + x * b) = b(a + x) + -1b
(1b + bx) = b(a + x) + -1b
1b + bx = (a * b + x * b) + -1b
1b + bx = (ab + bx) + -1b

Reorder the terms:
1b + bx = ab + -1b + bx

Add '-1bx' to each side of the equation.
1b + bx + -1bx = ab + -1b + bx + -1bx

Combine like terms: bx + -1bx = 0
1b + 0 = ab + -1b + bx + -1bx
1b = ab + -1b + bx + -1bx

Combine like terms: bx + -1bx = 0
1b = ab + -1b + 0
1b = ab + -1b

Solving
1b = ab + -1b

Solving for variable 'b'.

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

Add '-1ab' to each side of the equation.
-1ab + 1b = ab + -1ab + -1b

Combine like terms: ab + -1ab = 0
-1ab + 1b = 0 + -1b
-1ab + 1b = -1b

Add 'b' to each side of the equation.
-1ab + 1b + b = -1b + b

Combine like terms: 1b + b = 2b
-1ab + 2b = -1b + b

Combine like terms: -1b + b = 0
-1ab + 2b = 0

Factor out the Greatest Common Factor (GCF), 'b'.
b(-1a + 2) = 0

Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Simplifying
b = 0
Subproblem 2
Set the factor '(-1a + 2)' equal to zero and attempt to solve:

Simplifying
-1a + 2 = 0

Reorder the terms:
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

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

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

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

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

Simplifying
0 = -2 + a

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
b = {0}