A Clean Equation

 is a Railroad radiant quest in Fallout 4. It requires the Sole Survivor to go to a random location and eliminate a Brotherhood Patrol.

Quick walkthrough
1. Eliminate the Brotherhood Patrol

2. Report back to Predictive Analytic Machine

Detailed walkthrough
1. Eliminate the Brotherhood Patrol

Your Pip-Boy will have been updated with the location of the Brotherhood Patrol (they are different random locations). Travel to that location and eliminate the Brotherhood Patrol however you see fit. A patrol consists of 3 Brotherhood soldiers of variable ranks.

2. Report back to Predictive Analytic Machine

Return to P.A.M. at the Railroad HQ. She will congratulate you on a job well done and give you 130 bottlecaps.