解 （カイ） solution (of an equation, inequality, etc.), root (e.g. of a polynomial), solution (to a given problem), answer, explanation, interpretation

解禁 （カイキン） lifting a ban, raising an embargo, opening a season (hunting, fishing, etc.), publishing contents, revealing information

瓦解 （ガカイ） collapse, downfall

明解 （メイカイ） clear explanation

解熱 （ゲネツ） lowering a fever, alleviation of fever

解脱 （ゲダツ） liberation from earthly desires and the woes of man, deliverance of one's soul, moksha, mukti, vimukti

雪消 （ユキゲ） snow melting, water from melting snow

義解 （ギゲ） explanation (of the meaning), interpretation

解く （とく） 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)

溶かす （とかす） to dissolve, to melt

梳かす （とかす） to comb out, to brush, to untangle, to unravel

解ける （とける） 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

溶ける （とける） to melt, to thaw, to fuse, to dissolve

解く （ほどく） to undo, to untie, to unfasten, to unlace, to unravel, to loosen, to unpack

解ける （ほどける） to come loose, to come untied, to come undone, to unravel, to loosen up (e.g. tension)

分かる （わかる） to understand, to comprehend, to grasp, to see, to get, to follow, to become clear, to be known, to be discovered, to be realized, to be realised, to be found out, I know!, I think so too!