How do you solve #4x^2=13x+12#?
Find the factors of 4 and 12 which subtract to give 13.
However, 13 is an odd number which can only happen from the difference between an odd and an even number. This is a clue that the factors of 4 are not 2 and 2, because any product of these even numbers will give even numbers.
Similarly the factors of 12 are not 2 and 6, because they are both even. We find the following cross products and subtract them:
However, we need -13, so the combination must be -16 and +3.