ab+a=1fora

Solution for ab+a=1fora equation:

Simplifying
ab + a = 1fora

Reorder the terms:
a + ab = 1fora

Solving
a + ab = 1afor

Solving for variable 'a'.

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

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

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

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

Simplifying
1 + b + -1for = 0

Solving
1 + b + -1for = 0

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

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

Reorder the terms:
1 + -1 + b + -1for = 0 + -1

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

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

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

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

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

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

Simplifying
0 = -1 + -1b + for

The solution to this equation could not be determined.

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