解ける

1. ichidan verb, intransitive to be solved; to be worked out
2. to come loose; to come untied; to come undone
3. to be removed (of restrictions); to be lifted (e.g. of a ban); to be broken (of a spell, curse, etc.)
4. to dissipate (of anger, tension, etc.); to melt away; to ease; to be allayed; to be appeased; to be resolved (of a dispute, misunderstanding, etc.); to be cleared up

also 溶ける · 融ける

1. ichidan verb, intransitive to melt; to liquefy; to soften (e.g. through heat); to thaw
2. to dissolve (in a liquid); to be soluble (in)
3. colloquial to be used up (of money or time); to be wasted; to melt away

ほどける

1. ichidan verb, intransitive, usually in kana to come loose; to come untied; to come undone; to unravel
2. usually in kana to loosen up (e.g. tension)