after many twists and turns; after much trouble
Describes a process or journey that involved many complications, difficulties, or changes of direction before reaching a conclusion. Often used in narratives or explanations.
After many twists and turns, the project was finally completed.
After much trouble, the two ended up getting married.
Noun meaning 'twists and turns' or 'complications'; 紆余曲折を経て is the adverbial phrase form meaning 'after going through twists and turns'.
From the four-character compound 紆余曲折 (uyokyokusetsu, 'twists and turns') + を経て (o hete, 'passing through'). The compound itself is a yojijukugo combining 紆 (winding), 余 (excess), 曲 (bend), and 折 (break/fold).