Help solving recurrence relation, $a_n = 3a_{n-1} + 4a_{n-2} - 12a_{n-3}$ This is in my homework, and I am not sure how to go about this, I've read the book but I can't seem to grasp what to do. Help?
$$a_n = 3a_{n-1} + 4a_{n-2} - 12a_{n-3}$$
where $a_0 = 2$, $a_1 = -1$, $a_2 = 3$

Hint: the characteristic polynomial $x^3-3x^2-4x+12$ factors as $(x-3)(x-2)(x+2)$.
