ab+ca=abc

Solution for ab+ca=abc equation:

Simplifying
ab + ca = abc

Solving
ab + ac = abc

Solving for variable 'a'.

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

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

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

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

Simplifying
b + -1bc + c = 0

Solving
b + -1bc + c = 0

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

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

Reorder the terms:
b + -1b + -1bc + c = 0 + -1b

Combine like terms: b + -1b = 0
0 + -1bc + c = 0 + -1b
-1bc + c = 0 + -1b
Remove the zero:
-1bc + c = -1b

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

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

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

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

Simplifying
0 = -1b + bc + -1c

The solution to this equation could not be determined.

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