Question 278373
{{{p=q^2+5q+2}}} Start with the given equation.



{{{-2=q^2+5q+2}}} Plug in {{{p=-2}}}



{{{0=q^2+5q+2+2}}} Add 2 to both sides 



{{{0=q^2+5q+4}}} Combine like terms.



{{{q^2+5q+4=0}}} Rearrange the equation.



{{{(q+4)(q+1)=0}}} Factor the left side.



{{{q+4=0}}} or {{{q+1=0}}} Use the zero product property



{{{q=-4}}} or {{{q=-1}}} Solve for 'q' in each equation.



So the solutions are {{{q=-4}}} or {{{q=-1}}}