A Clean Equation

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) Try to persuade the patrol to join the Railroad.
 * 2) Send a peace offering in the form of a explosive.
 * 3) Eliminate the Brotherhood Patrol.
 * 4) 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.

Bugs

 * Even if the player is not hostile with the Brotherhood of Steel after finishing the game, P.A.M will assign them this quest. It also shares this bug with another radiant quest, High Ground which P.A.M can also assign.
 * It is possible for the Brotherhood Patrol to die before the player reaches them, which does not fail the quest but will seemingly cause it to break. There is no apparent way to complete A Clean Equation should this happen, though PAM will dispense new quests.

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