Deleting an object when multiple pointers are pointing to it?

I've been told that when if I have multiple pointers pointing to the same object, I cannot delete it normally (using the delete keyword). Instead, I've been told that I need to set the pointers to NULL or 0.

Given I have:

ClassA* object = new ClassA();
ClassA* pointer1 = object;
ClassA* pointer2 = object;

So to delete pointer1 and pointer2, do I need to do the following?

pointer1 = 0;
pointer2 = 0:

Once I've set it to NULL, do I still need to use the keyword delete? Or is just setting it to 0 good enough?