[alanctgardner]

But the point of this site is seemingly "understanding", not an algorithm - see the title of the page ("right, not rote"). However, what they really seem to be doing is breaking down what should be an intuitive process - understanding equalities and how to work with them - into several smaller, vague sub-processes which also aren't really easy to understand. I would argue that explanations like this might hurt someone's chances of understanding concepts like systems of equations later on.

[pavel_lishin]

I thought it was meant to give us an intuitive explanation for why we approach things via the "factoring algorithm" as a method of solving these guys.

In any case, it's just a simple example case. x^2 + x = 6 can probably be solved just by staring at it for a little bit, but once the equation gets more complex, trying out a couple of numbers in the [-5,5] range is not gonna work anymore.