Hi Paige 20, welcome to rootschat!
I checked on familysearch, and it appears your Solomon Holmes b 1846 in Howden (remember this is when the birth is registered, so the month doesn't have to reflect the actual birth date) is a 5 yr old 'pauper' in the 1851 census and 14 yr old apprentice in 1861. (I'm not on ancestry either, but someone else might be able to look these up for you.) In 1871 he's living in Nottinghamshire with
Solomon Holmes, self, 24, b Oden, Yorkshire
Elizabeth Holmes, wife, 23, b London, Nottinghamshire
William, son, 4, b Nottingham
George, son, 2, b Derby
Albert, son, 0, b Retford.
I'm assuming he went to Ohio? I noticed some other records for marriage and death of his children, including the George and William in the 1871 census.
Will keep looking for his parents