How did Brown v. Board of Education redefine the meaning of "equal protection of the laws" from the Fourteenth Amendment?

Until Brown v Board of education, the equal protection of laws clause was believed to be in favor of segregation since the separate but equal doctrine was considered valid if everyone got equal resources. However, during the case it was decided that segregation was opposed to the equal protection of the laws and the 14th amendment since any segregation is inherently unequal regardless of who's doing it and why. Having segregated public schools was then against the 14th amendment and it was forbidden.