そんなわけで

that's why

→ そんな
phrase Rare #36,231
that's why Used to introduce a result or conclusion based on something mentioned previously; it can also mean “for that reason.”
JA: そんなわけで、今日は早く帰ります。
EN: That's why I'm going home early today.

そんなわけでハリウッド出てきた

That's how I ended up in Hollywood.

— マルホランド・ドライブ (2001)

そんなわけで彼はほとんど言うことがなかった

That being the case, he had very little to say.

そんなわけで私は昨日学校を休んだのです

That's why I was absent from school yesterday.

そんなわけでオーストラリアは嫌いだったんだ

That’s why I hated Australia.

そんなわけで私は昨日授業に遅れたのです

That's why I was late for class yesterday.