Goodwin attended Sylvan Hills High School in Sherwood, Arkansas where he played for coach Kevin Davis and led his team to back-to-back state finals.

[5] Two days later, he narrowly missed the second triple-double in UK history against LIU-Brooklyn with 22 points and career highs of nine rebounds and nine assists.

[8] On July 12, 2013, he signed his rookie scale contract with the Suns and joined them for the 2013 NBA Summer League.

However, in Goodwin's second game against the Utah Jazz on November 1, he scored his first NBA field goal.

[15] In the Suns' final game of the season, Goodwin scored a career-high 29 points in a 104–99 win over the Sacramento Kings.

[16] After managing just 10 games for the Suns to start the season, Goodwin was reassigned to the Bakersfield Jam on December 25, 2014.

[20] He once again had an impressive regular season finale for the Suns, scoring a season-high 18 points in a loss to the Los Angeles Clippers.

In that game, Goodwin hit a three-pointer from atop the arc with 0.1 seconds left to lift the Suns over the Hawks with a 98–95 win, ending a six-game losing streak.

[27] On February 10, in a game against the Golden State Warriors, Goodwin and teammate Markieff Morris got into a physical altercation on the bench and were seen arguing during a timeout.

[28] Goodwin was released by the Suns on October 24, 2016, prior to the start of the 2016–17 regular season, in a move that was considered unexpected by many in the NBA.

[32] He made his debut for the Pelicans five days later, scoring seven points off the bench in a 126–99 loss to the Los Angeles Lakers.

[35] The next day, he made his debut for the Swarm in a 121–106 loss to the Texas Legends, recording 18 points, six rebounds and one assist in 29 minutes.

[39] In the Nets' season finale on April 12, 2017, Goodwin scored a season-high 20 points in a 112–73 loss to the Chicago Bulls.

On October 19, 2018, he was traded to the Maine Red Claws in exchange for the rights to Daniel Dixon,[44] but did not make the team's final roster.

In addition, his father, Archie Goodwin II, played college basketball for Arkansas State University.