3x2-10x-8=(3x+2)(x-4),
(3x+2)(x-4)>0 implies (a) 3x+2<0 and x-4<0; or (b) 3x+2>0 and x-4>0.
If (a), 3x<-2, x<-⅔ and x<4. Since -⅔<4 the solution to (a) is x<-⅔;
If (b), x>-⅔ and x>4. Since 4>-⅔ the solution to (b) is x>4.
Therefore the solution to the inequality is x<-⅔ or x>4.