Information taken from military record:

Solomon Bacon
age 18
Blue eyes
light hair
light complexion
5' 10" tall
born at Wayne Co., New York
Occupation- Farmer
Enlisted on April 23, 1847 at Jackson, MI
Private Company E 15th regiment enrolled by Lt Titus Platt
Discharged at expiration of service on August 6, 1848 at Cinncinnati, Ohio

Found on Return of Capt Thomas W. Freelon's Company E, 15th Regiment of United States Infantry for January, 1848:
Return lists Solomon Bacon acting as Hospital Attendant stationed at El Molino del Rey, Mexico. The Battle of El Molino del Rey was one of the bloodiest engagements of the Mexican-American War. It was fought in September 1847 between Mexican forces under General Antonio Léon against an American force under General Winfield Scott at El Molino del Rey near Mexico City. Several members of Company E listed as dead at the battle of El Molino del Rey and the storming of Chapultepec.

From Jackson Citizen (Michigan) Tuesday Oct 7, 1884 pg 1
Henrietta Township
Solomon Bacon, a veteran of the Mexican war, is entitled by a late act of congress to $12 a month pension. Mr Bacon was in the battle of Palo Alto, fought on the eighth and ninth of May, 1846, where the Americans 5,000 strong, mostly volunteers, under the command of Gen. Taylor, were victorious over the Mexicans 40,000 strong, under the orders of Santa Anna.
(Question: How could Solomon Bacon have been in Mexico at the Battle of Palo Alto in May, 1846 if he didn't enlist until April, 1847?)

Solomon Bacon (Private)