By factorising, solve the quadratic equation x^2-8x+15=0

First we find two numbers that that add up to -8 and multiply to make 15. In this case the numbers are -3 and -5. This means we can now factorise the quadratic to give (x - 5) (x - 3) = 0. For the above to be true, either (x - 3) = 0 or (x - 5) = 0. So x = 3 or x = 5.