solve for p

If $1/3 p+1/2 p+7=7/6 p+5+4$, then the first step is to remove the fractions. Multiply by 6 to get

$2p+3p+42=7p+30+24$. Combine like terms to get

$5p+42=7p+54$. Then subtract $5p+54$ from both sides to get

$-12=2p$. Next, divide both sides by $2$ to get

$p=-6$, and we have the answer.