Can braces fix multiple missing teeth gap? (photo)

Im 26 years old, i have always had dental problems since my younger age. Had to extract 6 teeth, 3 upper and 3 lower. Do you think braces can fix it to close the space like protract my molars. I dont want implant, bridge or prothesis. I would consider the prothesis in case braces cant. I dont really care about the time process. I just dont want to deal with implants. And will i have to extract more for the braces? Thank you

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