If the factors of the polynomial were (x-5) and (x-6), the values of x that would make the polynomial equal to zero would be 5 and 6.
5 - 5 = 0
6 - 6 = 0
Assuming the polynomial is (x-5)(x-6), if one factor is 0 then anything multiplied by 0 is still 0.
Hope this helps!