A family of transmissions incorporating three planetary gearsets and five torque-transmitting mechanisms is effective in a powertrain to produce at least six forward speed ratios and one reverse speed ratio between a transmission input shaft and a transmission output shaft. The planetary gearsets each have three planetary gear members in which two of the planetary gearsets have two members continuously interconnected and one of those planetary gearsets and the remaining planetary gearset have two members continuously interconnected. The remaining planetary gearset has one member continuously connected with the transmission housing and the transmission output shaft is continuously connected with at least one member of the planetary gearsets. The planetary gearsets have members that are selectively interconnected with the transmission input shaft through three selectively engageable torque-transmitting mechanisms. One other selectively engageable torque-transmitting mechanism provides a brake or a clutch element for the members of the planetary gearsets. A fifth of the selectively engageable torque transmitting mechanisms provides a brake for the planetary gearsets. The torque-transmitting mechanisms are engaged in combinations of two to establish at least six forward speed ratios and one reverse speed ratio between the transmission input shaft and the transmission output shaft.