To do that, you need to set it all to zero and factor:
x^2+8x+15 = 0
(x+5)(x+3) = 0
then put both those in parentheses chunks in their own equations
x + 5 = 0
x + 3 = 0
and then simplify
x = -5
x = -3
So the two points where the parabola crosses the x-axis are -5 and -3.