[tex]\frac{2p}{9}+\frac{5p}{18}-\frac{5}{6}=\frac{2}{3}+\frac{p}{12}+\frac{1}{6}\ \ \ |Multiply\ by\ 36\\\\
4*2p+2*5p-5*6=12*2+3*p+6*1\\\\
8p+10p-30=24+3p+6\\\\
18p-30=3p+30\ \ \ |Subtract\ 3p\\\\
15p-30=30\ \ \ |Add\ 30\\\\
15p=60\ \ \ |Divide\ by\ 15\\\\
\boxed{p=4}[/tex]
