Solving 6th-Degree Polynomials Using Ezouidi’s Theorem

For centuries, polynomial equations have been the most elegant expression of mathematical truth — yet their exact solutions have remained elusive. After 1824, Abel’s theorem was interpreted as a permanent barrier: beyond degree four, algebraic formulas cease to exist. Cardano solved the cubic, Ferrari solved the quartic, Lagrange reorganized known methods, and Galois theory described the symmetry of solutions. But none of these approaches produced a universal technique for degrees five, six, seven, or twenty. Modern mathematics shifted toward numerical approximations, iterative algorithms, and computational heuristics. The search for exact solutions faded. Ezouidi’s Theorem restores algebraic solvability. It introduces a discriminant-driven framework that systematically decomposes any polynomial into solvable symbolic components. Rather than guessing transformations, the theorem derives internal invariants and recursive structures that generate radical and nested expressions with complete algebraic consistency.