Solve this existance condition without a 2nd grade inequation

[LeonardoAcquaroli]

Hi everyone!
I'm having trouble trying to find the existance conditions of y = $$\sqrt{x^4-5x^3+6x^2}*\sqrt[3]{-x}$$ without solving a 2nd grade inequation.
I find that the domain is $$-\infty,2];[3,\infty$$ and so the function does not exist between 2 and 3 and i find this solving $$x^2-5x+6\geq0$$.

Unfortunately this is not the aim of my test and I need to solve that existance condition with one (or more) first grade inequation.
Any hints?

Thank You in advance

 

[blamocur]

Does it help that $x^2-5x+6 = (x-3)(x-2)$?