** Find the solution of the following initial value problem: $$a_n=-12 a_{n-1}-48 a_{n-2} - 64 a_{n-3};a_0=0,a_1=-20,a_2=320$$

$a_n = \alpha_1(r)^n+\alpha_2n(r)^n+\alpha_3n^2(r)^n$

$\alpha_1=$

$\alpha_2=$

$\alpha_3=$

$r=$