How to solve -2p^2=16p+24

Add  2p²  to each side of the equation.  Then you have

                 2p² + 16p + 24  =  0 .

Before you roll up your sleeves and start working on it, you can make it
even more convenient if you divide each side by  2 .  Then you have:

                 p² + 8p + 12 = 0 .

Now you have a nice, comfortable, familiar-looking quadratic equation. 
You can either factor the left side into  (p + 6) (p + 2), or, if you can't find
the factors, you can apply the quadratic formula to it.

That's how to solve it, and find its two solutions.