We consider a class of functional differential equations with both discrete and distributed delays. Distributed delays are represented by integrals whose bounds are commensurate with the discrete delays and by weight functions which are impulse responses of finite-dimensional time invariant linear systems. The properties of such systems can be studied by using simple algebraic techniques (polynomials in one variable). Under the natural assumption of spectral controllability, we give an explicit algebraic algorithm to compute a control function which steers any given initial datum to the equilibrium position in finite time. This algorithm also constitutes a direct constructive and simple proof that spectral controllability implies null controllability for the class of systems considered. The algorithm requires, after the computation of the roots of a polynomial in one variable, a finite number of steps.