  Undergraduate students of mathematics continue to solve equations in
virtually any course they attend, just as they did in secondary school -- yet
what do they learn about equations and their solutions at university? Are they
capable to combine elements of abstract algebra and real analysis to assess
what it means to solve an equation, in particular, what it means for an
equation to be solvable -- or not? In this paper, we present a mathematical and
didactical analysis of these questions, illustrated by examples from a capstone
course for future Danish high school teachers.
