You look at the factors of 9 and 5: we have 1 and 9, and 3 and 3; and we have 1 and 5. Then we look at the middle term coefficient which is 12. We note that the sign of 5 is negative, which means that we need a positive and a negative zero for the factors of the quadratic. We then try all the possibilities of combining factors of 9 and 5: so we have (1 9), (9 1) and (3 3) against (1 5) and (5 1), and we look for the combination that gives 12 when we play them off against one another. If (a b) represents the factors of 9 and (c d) the factors of 5 we're looking for the difference between ad and bc equals 12. The solution is (3 3) and (1 5) or (5 1) because 3*5-3*1=12. (Note that if the sign of 5 was positive we would be looking to find the right factors such that ad+bc=12.) Now we set up our factors in brackets: (3x 1)(3x 5) (that is, (ax c)(bx d)) without the signs. We have to end up with a minus in front of the 12 so we need to put the plus so that it's the smaller product that has the + sign, so 1 carries the plus and 5 carries the minus: (3x+1)(3x-5). This explanation sounds complicated, but it takes longer to explain it than to try it out! Practise and you'll find it gets easier.