Question 1040895
The x-value that will give the minimum value will just be the average of the two roots, namely -4 and 2p.  Their average is {{{(-4+2p)/2 = p-2}}}.

===> {{{2(p-2+4)(p-2-2p) = -18}}}, 

after direct substitution into the equation.

<===> (p+2)(-p-2) = -9  <===> {{{(p+2)^2 = 9}}} ===> p+2 = 3, or p+2 = -3

==> p = 1, or p = -5.