(AB)(AC)=ABC

Solution for (AB)(AC)=ABC equation:

Simplifying
(AB)(AC) = ABC

Multiply AB * AC
A2BC = ABC

Solving
A2BC = ABC

Solving for variable 'A'.

Reorder the terms:
-1ABC + A2BC = ABC + -1ABC

Combine like terms: ABC + -1ABC = 0
-1ABC + A2BC = 0

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

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

Simplifying
ABC = 0

Solving
ABC = 0

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

Simplifying
ABC = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-1 + A)' equal to zero and attempt to solve:

Simplifying
-1 + A = 0

Solving
-1 + A = 0

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

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

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

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

Simplifying
A = 1
Solution
A = {1}