Solomon's ship was intercepted by a Silurian Ark which had crossed his route. He sent out a distress signal and was picked up by the Silurians. He discovered that they were transporting dinosaurs upon their Ark and quickly set about taking them for his own. He ordered his two robots to wake the Silurians from stasis in small groups and then dispatched them into space.
However, he realised later that the ship had reset its course back to where it came from - Earth. When the Eleventh Doctor arrived, he realised that he finally had a means of changing course and of repairing his legs, which had been mauled by Velociraptors. The Doctor repaired his legs, but then Solomon betrayed him, demanding the Egyptian queen Nefertiti, otherwise his two Robot Mercenaries would blast the Doctor and his companions with their lasers. The Doctor obliged after Solomon's Robots killed the Triceratops, and Solomon took Nefertiti to his small space vessel in hope of escape, as Earth had locked missiles onto the ship. He failed to demagnetise and needed the Doctor's aid.
The Doctor returned but shut down the Robots and placed the homing device in Solomon's ship, so that the missiles would hit it instead. The Doctor took Nefertiti and demagnetised the ship, allowing it to fly out of the Ark. Solomon then died when his ship was blown up by the missiles. (TV: Dinosaurs on a Spaceship)
The Great Intelligence mentioned, among others, the death of "Solomon the trader" at the hands of the Doctor to dispute Madame Vastra's claim that the Doctor was never "blood-soaked". (TV: The Name of the Doctor)
Solomon was a true sociopath. He was greedy and ruthless and showed his brutality by killing all the Silurians that lived on the Ark. Although he thanked the Doctor for repairing his legs, he showed that he was willing to put the Doctor's friends in harm's way in order to get what he wanted. Solomon treated Queen Nefertiti as an object of high value and showed no concern or emotion for the lives of others. He was not above trying to manipulate others' emotions, and begged the Doctor not to leave him behind when the Doctor sent his ship into space, with Solomon still on board, in order to draw away missiles that had been fired towards the ark. Solomon was both enraged and terrified when he realised that the Doctor had sent him to his death. (TV: Dinosaurs on a Spaceship)
Behind the scenes
Due to his Jewish-sounding name, avaricious personality, and stereotypical appearance, this character has been accused by some fans of being an anti-Semitic trope. However, director Saul Metzstein has denied intending this, claiming that Solomon's look was in fact modelled directly on Peter Stringfellow, an English businessman and nightclub owner. Peter Stringfellow, notably, is not known to be himself Jewish, and, although the name "Solomon" is of Semitic origin, there is no definite in-universe evidence as to even the species, let alone the background, of the character, although one could argue that regardless of his literal in-universe background he effectively "coded" as Jewish, but it is unclear as to whether this was accidental.