I'm stuck in the highlighted part of the problem....
I did not see that! Thank you.
asilvester635, your first line was $\displaystyle 4z^3= 4z^2+ 24z$. Your next line should be $\displaystyle -4z^3+ 4z^2+ 24z= 0$ (you have subtracted $\displaystyle 4z^3$ from both sides). But then you have "$\displaystyle 4z^3- 4z^2+ 24z$". My guess is that you intended to multiply by -1 but, again, you must have "= 0" and you did not multiply the "24z" by -1. You should have $\displaystyle 4z^3- 4z^2- 24z= 0$. Obviously both "4" and "z" divide each term so you can factor 4z out: $\displaystyle 4z(z^2- z- 6)= 0$. (3)(2)= 6 and their difference is 1 so we can further factor as $\displaystyle 4z(z- 3)(z+ 2)= 0$.
Now what? Remember the basic reason for factoring: "if ab= 0 then either a= 0 or b= 0".