How to solve a recursive equation I have been given a task to solve the following recursive equation
\begin{align*}
a_1&=-2\\
a_2&= 12\\
a_n&= -4a_n{}_-{}_1-4a_n{}_-{}_2, \quad n \geq 3.
\end{align*}
Should I start by rewriting $a_n$ or is there some kind of approach to solve these?
I tried rewriting it to a Quadratic Equation (English isn't my native language, sorry if this is incorrect). Is this the right approach, if so how do I continue?
\begin{align*}
a_n&= -4a_n{}_-{}_1-4a_n{}_-{}_2\\
x^2&= -4x-4\\
0&= x^2 + 4x + 4
\end{align*}

you have to get the descriminent of this trinome :
$$
r^2+4r+4 = 0
$$
which is $r= -2$
and search solution of this form : 
$$
(\alpha n+\beta)(-2)^{n}
$$
for your case :
you have to solve this system:
$$
a_n = (\alpha n+ \beta) (-2)^{n } 
$$
$$
a_0 = -2 
$$
$$
a_1 =  12
$$
it's a simple $2*2$ linear system you can solve it with cramer method or gauss pivot .
