Why do you think the cm^2 would be the correct unit for Ag?
Actually its length * time^2!! [Ag] = kg/ksc
But by dividing by the constant of gravity g you can write it as

which is probably what you actually have in mind.
The symbolic engine you use when you make usage of "solve" is a third party add-on and does not integrate that perfectly in the philosophy of Mathcad or Prime as it does not know anything about units, They are treated as unknown variables and thats the reason you can't change the "units" you get in the result of a symbolic evaluation.
Normally you could follow the symbolic evaluation by a numeric (=) one or assign the result to a variable and evaluate it numerically in an extra region and then you could change the units as usual.
But you can see that the units in the symbolic result are not printed in bold blue which means that they are not recognized as units. This would make a numeric evaluation fail!

There is a calculation option you can set and sometimes helps with a problem like this

And you are lucky as in your case it does help

If it doesn't it may also help to replace the global definition of the unit ksc by a normal definition.
But as you are just looking for a numeric result, a suitable option would be to use a numeric method instead of the symbolic one. Prime offers a solve block with "find" or the "root" function.
For instance the root function used by providing an initial guess value

or use the root function by providing a range for Ag

As you can see I replaced Ast by the appropriate expression in Ag twice.
If you need to see Ast or if it would be a lengthier and more complex expression, you would have to define it as a function of Ag:

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