Totally irrelevant, but the English here should be 'you need to read the explanation more carefully'.
(I'm not sure why... you can say 'I need to run quickly to the store' or 'I need to run to the store quickly', but it's always 'read the explanation carefully' and never 'read carefully the explanation'. That last phrase feel harshly unnatural even though the parts of speech are the same as the run to the store example. Maybe someone knows why. Perhaps it has to do with there being only word position and no prepositions involved.)
To the OP, you should commit the なければならない to memory as a phrase meaning 'must'. It is in fact a standard negative-conditional conjugation followed by a negative conjugation, and many similar patterns share the same meaning (Japanese is full of double negatives!) However that particular phrase is a very standard one, and if you know it by heart you also will be familiar with the conjugations used to build it.
That said, I feel that the whole topic has diverged from the original question. You wouldn't use a generic
'must' (なければならない・なければいけない・などなど) to translate a -conditional must- from English.
I don't think you can use 仕上がり for finishing a race either, but I'm not quite sure about that. If you did, I'm don't think that 最初 would the right meaning of first. Maybe in the right sentence it could be used for finish a race first. But I think you were looking more for a meaning like 一位. Always be sure to check unknown words in a dictionary with examples - you can use EDICT dictionaries (jisho.org / wwwjdic / the 'kotoba' cell phone app / the rikai-chan browser app, , etc. etc., although I prefer
Yahoo!辞書 - 国語・英和・和英および専門辞書の検索サービス However, you mustn't rely on the basic gloss from those dictionaries but check the example sentences included in those apps, or example sentences from tatoeba.org /
英語学習・TOEIC対策・英辞郎 on the WEB | アルク , or other such sentence databases. A good example sentence is worth ten paragraphs of definition.)
Anyway, on the original proposal, I'd suggest that you you would use something like '早く走らなければ勝利しない'. (If I don't run quickly I won't win -> I must run quickly to win). Of course I am only a student of the language myself and may be mistaken here. If my sentence is in error hopefully someone will correct it, but a point that I do have confidence in is that this pattern is common in translation - that is, the English 'I must A in order to B' becomes a double negative in Japanese 'AしなければBない'.