"elucidate..."

From Miriam-Webster.com:

To "elucidate" is to make something clear that was formerly murky or confusing - and it is perfectly clear how the modern term got that meaning. "Elucidate" traces to the Latin term lucidus, which means "lucid." "Lucidus" in turn descends from the verb lucēre, meaning "to shine." So "elucidating" can be thought of as the figurative equivalent of shining a light on something to make it easier to see. "Lucēre" has also produced other shining offspring in English. Among its descendants are "lucid" itself (which can mean "shining," "clear-headed," or "easily understood"), "lucent" (meaning "giving off light" or "easily seen through"), and "translucent" (meaning "partly transparent" or "clear enough for light to pass through").

elucidate:  make (something) clear; explain.
"work such as theirs will help to elucidate this matter" 
- synonyms:explain, make clear, illuminate, throw/shed light on, clarify, clear up, sort out, unravel, spell out;