Answer
$$p=0,\:p=-\frac{3}{4},\:p=\frac{3}{4}$$
Work Step by Step
Solving the equation by factoring and setting the factors equal to zero, we find:
$$48p^5-27p^3=0 \\ 3p^3\left(4p+3\right)\left(4p-3\right)=0 \\ p=0,\:p=-\frac{3}{4},\:p=\frac{3}{4}$$
