Rien, and other negative pronouns/adverbs (personne, jamais, plus...) behave a bit weirdly in Fench: they replace the negative adverb "pas", and are placed exactly where it would be:

Je ne bois pas (I don't drink) -> Je ne bois rien (I don't drink anything)

Il ne voit pas (he doesn't see) -> Il ne voit personne (He doesn't see anyone)

Tu ne regardes pas la télé (You don't watch TV) -> Tu ne regardes jamais la télé (You never watch TV)

Nous n'avons pas vu (We didn't see) -> Nous n'avons rien vu (We didn't see anything)

This basically means that "pas" and "rien" don't come together (except in double negatives, as in "Je n'ai pas rien vu" = "I didn't see nothing", i.e. I did see something), and that rien, just like pas, comes between the auxiliary (here "va") and the verb (here "changer") in a compound tense:

Cela ne va pas changer (This won't change) - Cela ne va rien changer (This won't change anything)

There is one exception to this: "personne" when used with a compound verb (auxiliary + past participle or auxiliary + infinitive) comes after both elements, unlike "pas":

"Je n'ai pas vu", "Je n'ai rien vu", but "Je n'ai vu personne"

"Je ne vais pas voir", "Je ne vais rien voir", but "Je ne vais voir personne"

I hope I helped you, I know all these rules can be confusing so tell me if you have questions ^^