What would the rate equation be for this process?

$1)$E$+$S$->$ES

$2)$ES$->$E$+$S

$3)$E$+$C$->$EC

$4)$EC$+$S$->$ECS

$5)$ES$+$C$->$ECS

$6)$ECS$->$E$+$P$+$C

Make assumptions similar to the Michaelis$-$Menten and derive the rate equation in terms of $[$E$\_$Total$],[$S$],[$C$],$ and rate constants.