The way to solve this is apparently to use division by the common factor which is 3x^2
However, if I solve it with out the division like this (see below), I get the same answer. So what rule should I be following? Am I skipping steps or am I using different method?
You cannot 'solve' it anyway because it is not an equation; rather just an expression.
So I think you mean 'simplify' it.
It factorises (factorizes) as you have correctly done in your last line. That's it done.
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei