Given that $$(m+n+p)(mn+mp+np)=25$$ and that $$m^2(n+p)+n^2(m+p)+p^2(m+n)=4$$ for real numbers $m$, $n$, and $p$, what is the value of $mnp$?
(m + n + p)(mn + mp + np) = 25
m^2n + mn^2 + mnp + m^2p + mnp + mp^2 + mnp+ n^2p + np^2 = 25
[m^2(n + p) + n^2(m + p) + p^2(m + n)] + 3(mnp) = 25
4 + 3mnp = 25
3mnp =21
mnp = 7
