Solving a recurrence relation with no real roots? $a_n - 2a_{n-1} -12a_{n-2} - 14a_{n-3} -5a_{n-4} = 0 $
I've tried a few method: 


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*setting the denominator to $1 -2x -12x^2 -14x^3 -5x^4$ and then finding the numerator by multiplying $(1 -2x -12x^2 -14x^3 -5x^4)*\sum a_nx^{n}$

*finding the roots of C(y) = $y^4 -4y^3 -12y^2 -14y -5$ 
What else can I do? 

A start: The given recurrence has characteristic equation $x^4-2x^3-12x^2-14x-5=0$. This has $x=-1$ as a solution.
Dividing our polynomial by $x+1$, we get $x^3-3x^2-9x-5$. Note that $-1$ is a zero of this polynomial. Continue.
