Solve for q
q\in \left(-\infty,-2\right)\cup \left(8,\infty\right)
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q+2<0 q-8<0
For the product to be positive, q+2 and q-8 have to be both negative or both positive. Consider the case when q+2 and q-8 are both negative.
q<-2
The solution satisfying both inequalities is q<-2.
q-8>0 q+2>0
Consider the case when q+2 and q-8 are both positive.
q>8
The solution satisfying both inequalities is q>8.
q<-2\text{; }q>8
The final solution is the union of the obtained solutions.
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