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.
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei