Question 925979
The requested expression may have more than just one possible value, but at least this analysis works:


{{{p^3+3p^2+3p-7=0}}}
and testing of roots using Rational Roots Theorem and synthetic division shows....


_______1_____|_______1______3_______3______-7
_____________|
_____________|
_____________|_____________1_______4________7
__________________________________________________
____________________1______4_______7_________0



Note the remainder  of  0.
The equation is {{{(p-1)(p^2+4p+7)=0}}}, with the found solution p=1.


You can use this to get a value for the expression {{{p^2+2p}}}.
{{{1^2+2*1}}}
{{{highlight(3)}}}.


No other real value for p.
The quadratic factor is not factorable in real numbers.
(Discriminant is {{{4*4-4*7=16-28=-12<0}}} .)