Factorise and solve x^2 - 8x + 15 = 0

In order to solve a quadratic equation by factorisation you must first find the two numbers which add up to - 8 and multiply to get 15. We can do this by trial and error - first listing all of the pairs of factors of 15 and seeing which add up to make 8. 1 and 15, 3 and 5, -1 and -15 and -3 and -5. 1+15 = 16, -1+-15=16 and 3+5=8  so none of these are the correct pair. However, -3+-5 = -8 so this works well. Next we need to factorise this by putting each factor into brackets like this (x-3)(x-5)=0. We know that any number multiplied by 0 is 0 so next we have to find the values of x which make each bracket, in turn, equal 0. For the first bracket we can works this out by rearranging x-3=0 to give us x=3. Similarly for the second bracket we rearrange x-5=0 to give us x=5. This is then the final solution: x=3 or x=5. We can check these answers by subsitituting these values for x back into the equation to ensure that we get the correct result. For x=3 the equation becomes (3 * 3) - (8 * 3) +15 = 9 - 24 + 15 = 0 which is correct. For x=5 the equation becomes (55) - (85) + 15 = 25 - 40 +15 = 0 which also solves the equation correctly.