In Brown, there are no separate opinions; which means there was no majority but a unanimity of votes behind the holding that segregation cannot equate equality. Chief Justice Warren delivered the unanimous decision of the Court.
Of course, sometimes you may read a case without needing to focus on all of the aspects mentioned above. Keep in mind that you brief a case according to your own specific interests, and this is only one way in which you can read a case. It functions as an exercise in finding the decision within an opinion.