7MMPH0080VM0 Maytag Washer - Overview

First pry off the cap of the agitator. Then using a socket remove the bolt that holds the plastic cup in place. Remove this cup by prying it loose from the two tabs that hold it in place. Once this cup is removed you can get to the broken cogs.
Slip the new cogs into the underside of the cup, and slide the cup back down in the agitator housing using the slots on the side for a guide. (You may want to remove the entire agitator and assemble everything upside down, then flip it all back over to mount, so the cogs don't fall out).
Tighten the bolt, snap the cap back in place on top of the agitator and your'e done. Easy repair.

researched potential causes, found cluch dust under the washer and determined that it wouldn't engage because clutch was too worn. ordered the assembly, removed agitator from inside the tub as it is connected to the gear shaft, turned washer on it's back for access to motor, unattached the direct drive water pump from the motor drive, unbolted the 3 gearcase mounting bolts and took the entire gearcase, shaft, motor, etc... together, out from under the washtub. the clutch slides off the gearshaft with a little fidgeting and the new assembly is easily installed where the previous was. put everything back together... then... spin spin! worked perfectly

If you load a washing machine unevenly, it will spin out of balance. But our washer seemed to make noise during the spin cycle regardless of how the load was distributed. I suspected that the suspension or balancing springs were getting tired, and ordered a replacement set.

First I disconnected the washer from the water and power supply, then I laid it on its back.

The tub rested on the back of the washer, making two of the three suspension springs relax, and they were pretty easy to pull out with pliers. After the first two were out, I had to support the tub with a couple 2x4s to relax the third suspension spring.

Installation was the reverse of removal - install the lower suspension spring, remove the 2x4s, then install the two other suspension springs.

The tub balancing spring was easy to replace, and probably wasn't the cause of the problem.

With $25 in parts and about 15 minutes, my washer spins much more quietly.