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Well, this is a bug.

Here is a workaround: omit the declare(..., constant) and tell solve to solve for x specifically.

solve(a*x^4/4!+a*x^2/2!+b*x-%pi*b+a+c, x);

=> (quickly returns a long expression)

I can't tell what is the problem here; simpler examples seem to get solved right away.

I've moved this to the bug tracker in hope of eventually resolving it.