When something happens by accident, it's inadvertent, or unintentional. The gas company assured you that the error in your bill was inadvertent and that they would fix it, but not before you blew off some steam.
If you break down the adjective inadvertent you find the word vert, from the Latin vertere, meaning "to turn." Advertent comes to mean "turning the mind to," and as the prefix in- means "not," inadvertent means “not turning the mind to,” or "not intending to." When your actions are inadvertent you're not paying attention to their consequences. Remember that inadvertent ends with -ent by remembering this sentence: “We inadvertently ripped the tent.”