Forgive me if this is all due to a mathematical error that's obvious to you; I'm merely an engineer. I've used FindRoot with success in the past, but never with this complex of an equation.

I did my best to explain everything in the blue text.

If it matters, I'm using the final version of MKraska's portable install: 0.99.7579

FindRoot error.sm (17.23 KiB) downloaded 28 time(s).

The plot problem is due to unit mismatch. Note that in plots, the independet variable always gets unit-free values (except in Maxima Draw plots, if you specify limits with units). Thus you have to make sure that the functions to graph get arguments with the correct dimension. If you define the function explicitly, then something like a(x m) will work. If it is just an expression, then use the substitution operator at() from the Custom Functions plugin.

The solver problem is due to mismatch between number of equations and variables.

The key to using the result of Solve() is the function Assign().