Answer
The solutions are $p=0$, $p=\frac{3}{2}$ and $p=-7$.
Work Step by Step
Given: $5p(2p-3)(p+7)=0$
Using zero-product property, we have
$5p=0$ or $2p-3=0$ or $p+7=0$.
Solving for $p$, we get
$p=0$ or $p=\frac{3}{2}$ or $p=-7$.
The roots are $p=0$, $p=\frac{3}{2}$ and $p=-7$.
