Set the factors equal to 0.
(5k - 3)(9 + k) = 0
The zero product property states that if two terms being multiplied have a product of zero, then at least one of them must be zero. In our case, this means we can set both (5k - 3) and (9 + k) equal to 0:
5k - 3 = 0
5k = 3
k = 3/5
9 + k = 0
k = -9
The value of k is 3/5 and -9.