bx+b=ba+b

Solution for bx+b=ba+b equation:

Simplifying
bx + b = ba + b

Reorder the terms:
b + bx = ba + b

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

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

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

Solving
bx = ab

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 + bx = ab + -1ab

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

Factor out the Greatest Common Factor (GCF), 'b'.
b(-1a + x) = 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 + x)' equal to zero and attempt to solve:

Simplifying
-1a + x = 0

Solving
-1a + x = 0

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

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

Combine like terms: -1a + a = 0
0 + x = 0 + a
x = 0 + a
Remove the zero:
x = a

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

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

Simplifying
0 = a + -1x

The solution to this equation could not be determined.

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