If f(x) = 0 then
So basically you have some stuff multiplied together to make 0. This means that one of the things you multiply must be 0.
The 3 is not 0. The (x+6) might be 0. The (x+5) might be 0.
So x = -6 or -5. These are the roots of the function.
The multiplicity is how many times each root occurs in the factorization of the function. So since
The roots are x = -6 (mutiplicity 1), and x = -5 (multiplicity 4)