Ab+c=ba+c

Solution for Ab+c=ba+c equation:

Simplifying
Ab + c = ba + c

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

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

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

Solving
bA = 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 + bA = ab + -1ab

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

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

Simplifying
-1a + A = 0

Reorder the terms:
A + -1a = 0

Solving
A + -1a = 0

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

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

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

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

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

Simplifying
0 = -1A + a

The solution to this equation could not be determined.

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