50w Solar panel and charger install help

You question got a lot of answers with the word, Should, in it.

Should does not cut it. Anyone know for sure?

In theory, if the plugged-in charger just puts out a blind voltage then nothing will alter that, it will put out the voltage as long as it is plugged in.
The solar controller (unless u got a super cheap-o one) should be sensing the charge level on the batteries and adjust the type of charging it is doing according to the voltage. Low voltage means an aggressive charge, high means a float charge.
The plugged-in charger will fool the solar controller to think there is 14 volts (or whatever the charger puts out). A good battery will be closer to 13.6 volts or so, so less than the charger. The solar controller will always see a fully charged battery, so will likely be doing nothing except preventing solar voltage from charging. - Not a big deal since there is 14 volts charging happening from the plugged-in one.
So, I theorize they do not work together, rather one cancels out the other.
If you got a cheap-o solar controller then maybe it put its voltage to the battery and the plugged-in one puts its voltage to the battery and the only one that maters is whichever one is giving more voltage.
Now, if they are both smart chargers then we need a new theory.

Boon Docker wrote:
As Ivylog says there should not be a problem. They will both add to the charging.

Great!

Yes, they should work together fine. Fifty watts seems hardly worth the effort.

As Ivylog says there should not be a problem. They will both add to the charging.

Ivylog wrote:
They should work together without problems.

Great! Thanks, for the response.

They should work together without problems.