Finding moment for a beam that is fixed at both ends

[zewei1988]

I am curious as to how to find the moment at both of the fully fixed end (something like cantilever) of a beam.

The details of the beam are as follow:
The beam is 5m long
It is fully fixed at both ends
The first distributed load starts at 1.35m from the left, and ends at 1.65m from the left. It has a distributed load of 3.27kN/m.
The second distributed load starts at 3.35m from the left, and ends at 3.65m from the left. It has the same distributed load.

I have been trying to understand how the program managed to get the moment at both ends of the beam, but to no avail.

 

[SteamKing]

This is one procedure: https://www.physicsforums.com/attachment.php?attachmentid=39093&d=1316481731