Simplify and solve the following equation: x^2 -8x +15=0

Simplify the equation first by putting the x^2 into brackets. I do this by finding two values that both multiply to get 15 and add to get -8. I can see that -3 and -5 fit this criteria, but i could easily go through each set of values until i get the ones that fit if this wasn't as obvious. I then put this into bracks with each x value, giving: (x-3)(x-5)=0. I then put each bracket equal to zero to find each x value. x-3=0 and x-5=0, meaning x= 3 and 5