In high school, Coelho was involved in student activism, and presided over the Student Union of the Federal Technical School of Bahia. Coelho later graduated from the Federal University of Bahia, where he graduated with a master's degree in history.
In 2006, Coelho was a candidate for Governor of Bahia,[3][4] and in 2008 ran for Mayor of Salvador. In the latter election, he headed the Socialist Left Front, and obtained 51 thousand votes. In 2010, he was a candidate for state deputy, and reached almost 25 thousand votes.[5]
He was elected a member of the Salvador City Council in 2012, running with Hamilton Assis heading the PSOL municipal ticket. He received 16,408 votes (1.27% of those valid), running as a member of the "Enough of Selling Our City" coalition (PSOL-PCB).
After being reelected in 2016, Coelho decided to run for the Legislative Assembly of Bahia, and became the first ever PSOL state deputy in Bahia.[6][7] In 2020, he once again unsuccessfully ran for Mayor of Salvador.[8][9] His running-mate was Rosana Almedia, a local coordinator for the National Housing Struggle Movement (MNLM) and PSOL organizer.[10]