Recursive sequences and solutions

Question

Let $s_0$, $s_1$, $s_2$, . . . be a recursive sequence defined by

$s_0 = 4$,$s_1 =3$, $s_n$ =$−6s_{n−1}$ − $9s_{n−2}$ for all integers $n\ge2$

Find an expression for $s_n$ in terms of $n$ that holds for all integers $n \ge 0$.

So far I've got:

The characteristic equation of the recurrence is $x^2 + 6x + 9$

Factorised: $(x+3)^2 = 0$

double root $x=-3$

and this is where I'm stuck

Answer 1

$a_n = c_1(r^n)+c_2n^2(r^n) + ... + c_mn^{m-1}(r^n)$ is the general solution when the characteristic equation has m repeated real roots.