Yours, Etc.: Origins and Uses of 8 Sign-Offs
late 14c., "capable of being dissolved," from Old French soluble "expungable, eradicable" (13c.), from Late Latin solubilis "that may be loosened or dissolved," from stem of Latin solvere "loosen, dissolve" (see solve). Meaning "capable of being solved" is attested from 1705. Substances are soluble, not solvable; problems can be either.
soluble sol·u·ble (sŏl'yə-bəl)
Capable of being dissolved, especially easily dissolved.