If condition on $a$ is given, then find the domain of the function If $\log _{\frac{1}{3}} (|a|+1)>-1$, then find the domain of 
$$f(x)=\sqrt{2x^4+ax^3-6x^2-4ax-8}$$
Using $\log _{\frac{1}{3}} (|a|+1)>-1$, I got $-2<a<2$ but to use it in $\sqrt{2x^4+ax^3-6x^2-4ax-8} \geq0$
Could someone help me with this.

HINT:
$$2x^4+ax^3-6x^2-4ax-8=2x^4-6x^2-8+ax(x^2-4)=\\=2(x^4-3x^2-4)+ax(x^2-4)=2(x^2-4)(x^2+1)+ax(x^2-4)=(x^2-4)(2x^2+ax+2)\\$$
NOTE:For factoring $x^4-3x^2-4$ you can use the change of variables $t=x^2$ and use a quadratic.
