This document summarizes a study examining how academic engagement and interdisciplinary research relate to achieving both scientific impact and societal relevance. Negative binomial regressions on survey and publication data from Spanish scientists found that: 1) Academic engagement and interdisciplinary variety were positively associated with both societal relevance and scientific impact; 2) Interdisciplinary disparity was positively associated with societal relevance but its interaction with variety was positively associated with scientific impact; 3) Control variables like past impact, productivity and affiliations were also significant predictors. The study provides empirical evidence that engagement and interdisciplinary research can enhance complementarities between scientific and societal impacts.