ab+c=ab+ac

Solution for ab+c=ab+ac equation:

Simplifying
ab + c = ab + ac

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

Combine like terms: ab + -1ab = 0
0 + c = ab + -1ab + ac
c = ab + -1ab + ac

Combine like terms: ab + -1ab = 0
c = 0 + ac
c = ac

Solving
c = ac

Solving for variable 'c'.

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

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

Combine like terms: ac + -1ac = 0
-1ac + c = 0

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

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

Simplifying
c = 0

Solving
c = 0

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

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

Simplifying
-1a + 1 = 0

Reorder the terms:
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

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

Simplifying
0 = -1 + a

The solution to this equation could not be determined.

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