From main clauses, you may remember the verb bracket or Verbklammer — i.e., the finite verb (excluding removeable prefixes) is second and whichever parts of the word are missing come last.
Er wird nicht lesen.
Wir gehen nicht aus.
Ich habe das Buch gelesen.
Most of the sentence is then kept inside this bracket with principal exception of extended infinitives which are often placed behind it.
In subordinate clauses, the bracket as such still seems to exist, however, the finite verb has been moved even further to the back — at least that is how you can imagine it. Thus, you end up with a chain of verbs at the very end of any subordinate clause.
…, weil er nicht lesen würde.
…, weil wir nicht ausgehen.
…, weil ich das Buch gelesen habe.
(Note that separable verbs as in my second example are no longer separated in subordinate clauses.)
Attempting to put the negation particle nicht, which behaves like an adjective, between the infinitive and the finite verb, you would be disturbing the verb chain and the sentence turns wrong.