I'm from Hong Kong and I have a question related to your page http://www.purplemath.com/modules/solvquad.htm. x(x+5)=0. You mentioned that "But you can't divide by zero". I would like to clarify if you mean "divide by zero" is conceptually wrong, or divide by zero in this equation can only lead to answer of x=1 and can't lead to x=0 so it is not a good idea.
Another very simple one: x(x+1)=2x, find x. Similarly, x=0 or x=1 like this:
x(x-1)=0 <== same as your x(x+5)=0
If we solve like this:
We know that we can never find the answer of x=0 in this way, but is this way "wrong" or "not good"?
Also, if something like xy=3x^2, can we "dividing off the x" to achieve y=3x?
This is similar that x can be zero or not and "But you can't divide by zero" apply here or not?