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to be solved; to be resolved
to loosen; to come untied; to come undone
to be removed (of restrictions); to be lifted (e.g. a ban); to be broken (spells, curses, etc.)
to dissipate (of anger, tension, etc.); to melt away; to ease; to be appeased; to be resolved (of a dispute, misunderstanding, etc.); to be cleared up
「解ける」 has another reading with different meanings.
考え続けて難しい問題がやっと解けた。
The difficult problem was finally solved.
説明したおかげで彼の誤解が解けたようだ。
His misunderstanding seems to have been cleared.
謎が解けてすっきりした気分になりました。
The mystery was solved and I felt relieved.