Unmanned aerial vehicles (UAVs) in cellular networks have garnered considerable interest. One of their applications is as flying base stations (FBSs), which can increase coverage and quality of service (QoS). Because FBSs are battery-powered, regulating their energy usage is a vital aspect of their use; and therefore the appropriate placement and trajectories of FBSs throughout their operation are critical to overcoming this challenge. In this paper, we propose a method of solving a multi-FBS 3D trajectory problem that considers FBS energy consumption, operation time, flight distance limits, and inter-cell interference constraints. Our method is divided into two phases: FBS placement and FBS trajectory. In taking this approach, we break the problem into several snapshots. First, we find the minimum number of FBSs required and their proper 3D positions in each snapshot. Then, between every two snapshots, the trajectory phase is executed. The optimal path between the origin and destination of each FBS is determined during the trajectory phase by utilizing a proposed binary linear problem (BLP) model that considers FBS energy consumption and flight distance constraints. Then, the shortest path for each FBS is determined while taking obstacles and collision avoidance into consideration. The number of FBSs needed may vary between snapshots, so we present an FBS set management (FSM) technique to manage the set of FBSs and their power. The results demonstrate that the proposed approach is applicable to real-world situations and that the outcomes are consistent with expectations.