Solve in $\mathbb{R}$: $(x^2-3x-2)^2-3(x^2-3x-2)-2-x=0$
I'm supposed to solve this equation. It's from a math contest so solving it by hand would be preferable (no quartic formulas). I thought about making $u = x^2-3x-2$ obviously but it leads to another quartic equation. I also tried the substitution $u=x+2$, and after the whole expand trinomial, simplify, invoke rational root theorem and test roots, I still got nothing out of it.
I noticed that $x^2-3x-2$ can't be factored nicely so I dunno what other route to take. Lots of equations I tackled in math contests could make use of nice trigonometric substitutions, but none in particular pop in my head right now.
If anyone can give me hints or a full solution, that would be awesome. Thanks!