Find the zeros k(x) = -x²+ 2x + 15 explain every step!

Take out - 1
k(x) = -1(x^2 - 2x - 15) Now factor what's inside the brackets. The numbers you pick must add to - 2 and multiply to -15. 
When you multiply to -15 you should note that one of the numbers is plus and the other is minus.
(x -  )(x +  ) is the way it looks.
They differ by 2 and the "largest" one is minus. That means your answer is -5 and +3
k(x) = - (x - 5)(x + 3)
Now for the zeros.
x - 5 can be a zero
x - 5 = 0
x = 5

x + 3 = 0
x = - 3