quality:corruption, stylistic:style_transfer
Approach

The explicit solution of a real or complex equation of degree 1 is trivial. Solving an equation of higher degree n reduces to factoring the associated polynomial, that is, rewriting (E) in the form

where the solutions are then the z 1, …, z n {\displaystyle z_{1},\dots,z_{n}}. The problem is then to express the z i {\displaystyle z_{i}} in terms of the a i {\displaystyle a_{i}}.

This approach applies more generally if the coefficients and solutions belong to an integral domain.