ab+3a=a

Solution for ab+3a=a equation:

Simplifying
ab + 3a = a

Reorder the terms:
3a + ab = a

Solving
3a + ab = a

Solving for variable 'a'.

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

Add '-1a' to each side of the equation.
3a + -1a + ab = a + -1a

Combine like terms: 3a + -1a = 2a
2a + ab = a + -1a

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(2 + 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 '(2 + b)' equal to zero and attempt to solve:

Simplifying
2 + b = 0

Solving
2 + b = 0

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

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

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

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

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

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

Simplifying
0 = -2 + -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}