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to untie; to unfasten; to unwrap; to undo; to unbind; to unpack
to unsew; to unstitch
to solve; to work out; to answer
to dispel (misunderstanding, etc.); to clear up; to remove (suspicion); to appease
to dissolve (a contract); to cancel; to remove (a prohibition); to lift (a ban); to raise (a siege)
to release (from duty); to relieve; to dismiss
to comb (out); to card; to untangle (hair)
「解く」 has another reading with different meanings.
この難しい数学の問題を解くのは大変だ。
Solving this problem is difficult.
謎を解くための手がかりを探す。
I am looking for clues to solve the mystery.
誤解を解くために説明しました。
I explained to clear up the misunderstanding.