ab+a+b=b

Solution for ab+a+b=b equation:

Simplifying
ab + a + b = b

Reorder the terms:
a + ab + b = b

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

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

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

Solving
a + ab = 0

Solving for variable 'a'.

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

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

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

Simplifying
a = 0

Solving
a = 0

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

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

Simplifying
1 + b = 0

Solving
1 + b = 0

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

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

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

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

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

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

Simplifying
0 = -1 + -1b

The solution to this equation could not be determined.

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