How do I solve quadratic equations by factorization?

Consider the equation x^2+5x+6=0. In order to factorise this equation you first need to think of what numbers sum to make 5 (the coefficient of x) and whose product equals 6 (the number not multiplied by x). If you can't think of any pair of numbers which give those results, then the equation is unfactorizable, but still possible to solve. In this case, the equation can be factorised and the numbers are 2 and 3. Now the equation is factorised to (x+2)(x+3)=0, which can now be solved as either (x+2) or (x+3) must equal to 0. So, this gives two possible answers: x=-3 and x=-2.