ぜんぜん + [verb ない-form] ぜんぜん + [verb ます-stem] + ません ぜんぜん + [i-adj 〜い → 〜く] + ない ぜんぜん + [na-adj] + じゃない / ではない ぜんぜん + [noun] + じゃない / ではない
ぜんぜん (全然) means "not at all". It goes before a verb or adjective in the negative, and the sentence still has to end in ない or ません: ぜんぜん only makes the negative stronger.
An い-adjective takes its own negative, 〜くない; a な-adjective or a noun takes じゃない or the more formal ではない.
On its own, ぜんぜん answers a question with "not at all", and the negative is understood.
In casual speech ぜんぜん also goes before an affirmative, where it brushes a worry aside: the other person expects a problem, and you say there isn't one. ぜんぜんだいじょうぶ大丈夫 and ぜんぜんいい are the everyday cases.
In writing and formal speech, keep ぜんぜん with a negative. ちがう違う counts as a negative here, so ぜんぜんちがう違う, "completely different", is fine anywhere.