Yet another way: x(x- 6)< -6 is the same as which is the same as (I used the fact that [tex]a^2- b^2= (a- b)(a+ b)).
The product of two numbers is negative if and only if one is positive and the other negative. Since the two factors are "x- 3" plus and minus the same thing, obviously . The first must be positive and the second negative: we must have and .
From the first and from the second . Together, those give, as before, .
klik11, you English is excellent. Certainly compared with my (Put whatever language you want here)!