Hi, welcome to Physics! We aren't a homework help site, so I have temporarily deleted this complete answer to a homework-like question. – rob♦
I think that it is - in this case - counter-productive. OP completely solved their problem but because a logical mistake near the end of their solution they obtained a wrong result. They didn't ask for the correct result, they knew it.
Other answerer gives them a complete solution, by the OP were not satisfied with it (they didn't upvote that correct answer and in the comment they insist to know, where they made a mistake). They refuse other, simpler and correct solution(s), they only want to know their mistake.
My answer seems as a complete solution, but it only analyzed and approved individual steps, while didn't encounter and pinpointed the place with the error. Of course, it resulted to the correct result, already known to OP. It only repeated the OP's steps, givig them nothing new.
As I said, my answer was temporary deleted. I didn't know, what does it mean "temporary".
The question itself was putting on hold, which is pitty, in my humble opinion, because:
OP don't want to solve their homework for them. They wanted learn from their mistakes.