What you're actually doing for any trinomial (with any leading coefficient) is multiplying the first and last term and then splitting the middle term into those two numbers that multiply to the last term and add to the middle term. So 1 x 6 = 6, 2 x 3 = 6, 2 + 3 = 5, so when you break it down it would look like: x^2 + 2x + 3x + 6, in which you can split the terms into two each: (x^2 + 2x)(3x + 6) and then factor out the GCF.
So: x(x+2) 3(x+2), the numbers inside the brackets have to be the same. So when you put that together it's simply: (x+3)(x+2)
What you're actually doing for any trinomial (with any leading coefficient) is multiplying the first and last terms together, then splitting the middle term into two numbers that multiply to that product and add to the middle term. So 1 x 6 = 6, 2 x 3 = 6, 2 + 3 = 5, so when you break it down it'll look like this: x^2 + 2x + 3x + 6, and now you can break it down into two components: (x^2 + 2x) (3x +6)
now factor out the GCF: x(x+2) 3(x+2), the numbers inside the brackets have to be the same. So when you put it together, it's: (x+3)(x+2)
Guys that problem is really not hard if you can remember factoring in high school. For a trinomial where the first/highest term has a coefficient of 1 you can simply find 2 numbers that multiply to the last/lowest term and add to the middle term (in this case it's 2 and 3). Then you can simply do (x +/- number1)(x +/- number2), it will always result in a binomial term. So the answer is (x + 2)(x + 3).