Learn Turkish: Hayvanlar bitki bulmak için göç etmişti. - The animals had migrated to find plants.

It combines the past participle suffix -miş with the past tense marker -ti. For the verb göç etmek (to migrate), the root is et-. Adding -miş makes it etmiş, and adding -ti makes it etmişti. This double past structure creates the past perfect tense, meaning "had migrated".

Since the subject hayvanlar is plural, why isn't the verb plural like göç etmiştiler?

In Turkish, when a non-human plural subject like hayvanlar (animals) is explicitly stated, the verb usually remains singular. Adding the plural suffix to make it göç etmiştiler would sound unnatural here.

The translation says "plants", but bitki is singular. Why isn't it bitkiler?

When talking about a general category or an unspecified quantity of a direct object, Turkish commonly uses the singular bare form. Here, they are looking for "plant life" or "vegetation" in general, so bitki bulmak is much more natural than bitkiler bulmak.

What is the grammar behind bulmak için meaning "to find"?