Question: Why does simplify change solve?

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Please check the attached worksheet out. When I simplify the expression first, solve can yield a closed form solution(g1). Otherwise, it seems concerned about the complex solution(g2 or q), which is a bit messy. Though testeq shows they are same in real domain. Should we always "prepare" the target for solve command? How to if so? In addition, how can I simplify g1 to reach a simplified expression like g3, which is produced after I manipulate the initial solving target.

I also put a assume command in the beginning in case you want to know the specification of my problem.

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