なくてはいけない

Can’t Not Do
Verb/い Adjective なくて form + はいけない
Noun/な Adjective + じゃなくてはいけない

なくてはいけない is the negative verb form of てはいけない. It means “Can’t not do”→ “Must do”.
It is interchangeable with なければいけない, but it comes across as a little stronger due to not being softened by a conditional. Both statements are used hypothetically.

なくてはいけない is more likely to be used if the other person said they weren’t going to do something and you need to correct them. 

Examples

• 報告しなくてはいけない – You can’t not report it. – You have to report it. 
• 勉強しなくてはいけない – You have to study.
• 食べなくてはいけない – You have to eat it.
• この薬を飲まなくてはいけない – You have to take this medicine.
  
  

なくてはならない

なくてはならない is the negative verb form of てはならない. Like てはならない, the only difference is it is more likely to represent a societal rule or norm rather than a personal opinion.

• 仕事をきちんとしなくてはならない – You have to do your work properly.
• お客様の機嫌を取らなくてはならない – You have to play to the guest’s mood.