Finding the roots of polynomial equations is a fundamental problem inmathematics. This paper discovers that general polynomial equations can be simplifiedinto a canonical or standard form through Tschirnhaus transformations. A power seriesrepresentation consisting of coefficients in the canonical or standard form is a universalrepresentation of the roots of polynomial equations. If the series converges, a root of theequation is obtained. If the series does not converge, it can be further transformedthrough one or more Tschirnhaus transformations to obtain a convergent seriesrepresentation. This method is applicable to higher degree polynomial equations withreal and complex coefficients, avoiding the complex determination of whether they aresolvable in the radicals , and has universal significance. This advance returns theproblem of finding polynomial roots to the realm of pure algebra, using only polynomialtransformations and multivariable power series.