Why does this happen?

A=3 and b=2
A+b=c is the equation.
Multiplying both sides of the equation makes the equation a^2+2ab+b^2 which is equal to a^2+ab-ac=-ab-b^2+bc
Dividing by (a+b-c) we find a=-b or 3=-2
Why?

Very simple.

All kinds of crazy things happen when you divide by zero

(if A=3 and b=2, and A+b=c, then (A+b-c)=0)