Answer
$p=-7/6, -3$
Work Step by Step
$3+\frac{1}{2p+4}=\frac{10}{(2p+4)^2}$
$3+\frac{1}{2p+4}=\frac{10}{(2p+4)(2p+4)}$
$3+\frac{1}{2p+4}=\frac{10}{(2p*2p+4*2p+4*2p+4*4)}$
$3+\frac{1}{2p+4}=\frac{10}{(4p^2+16p+16)}$
$3+\frac{1}{2p+4}=\frac{10}{2(2p^2+8p+8)}$
$3+\frac{1}{2p+4}=\frac{5}{(2p^2+8p+8)}$
$3+\frac{1}{2p+4}=\frac{5}{(2p+4)(p+2)}$
$(2p+4)(p+2)*3+(2p+4)(p+2)*\frac{1}{2p+4}=(2p+4)(p+2)*\frac{5}{(2p+4)(p+2)}$
$(2p+4)(p+2)*3+(p+2)*1=5$
$(2p*p+2p*2+4*p+4*2)*3+p+2=5$
$(2p^2+4p+4p+8)*3+p-3=0$
$6p^2+24p+24+p-3=0$
$6p^2+25p+21=0$
$p=(-b±\sqrt {b^2-4ac})/2a$
$p=(-25±\sqrt {25^2-4*6*21})/2*6$
$p=(-25±\sqrt {625-4*6*21})/12$
$p=(-25±\sqrt {625-24*21})/12$
$p=(-25±\sqrt {625-504})/12$
$p=(-25±\sqrt {121})/12$
$p=(-25±11)/12$
$p=(-25±11)/12$
$p=(-25+11)/12$
$p=-14/12$
$p=-7/6$
$p=(-25±11)/12$
$p=(-25-11)/12$
$p=-36/12$
$p=-3$
