We will start by making each of the solutions a binomial which is equal to zero.
First solution:
x = 5
x - 5 = 0
Second solution:
x = -2
x + 2 = 0
Then we can multiply the two together using FOIL.
0 = (x - 5)(x + 2)
0 = x^2 - 5x + 2x - 10
0 = x^2 - 3x - 10
Since solutions (colutions as you like to call them) are found at f(x) = 0, the 0 can be replaced with f(x).
f(x) = x^2 - 3x - 10
