This paper explores the operation of a turbofan jet engine with afterburniner using the EES (Engineering Equation Solver) software and CFD simulation in Solidworks. The aim of the study is to present and provide insights into all components of an afterburning jet engine, demonstrating the analysis of results obtained from EES and the CFD simulation. The GE-F404 turbofan jet engine with afterburning is used as an example in this study. At the beginning of the paper, each part and component of the turbofan jet engine, along with their functions, is explained in detail. This includes the operation of the fan, low- and high-pressure compressors, combustion chamber, low- and high-pressure turbines, the afterburning process, nozzle, and the fuel used. Each section explains the characteristics and provides examples of specific parameters and their relationships. In the practical part of the paper, a schematic representation of the engine is shown, and values such as turbine work, compressor work, and net work are calculated using the EES software. All input data and resulting outputs are presented, with T-s and P-v diagrams created from them to perform a thermodynamic analysis. In addition to the EES program, a CFD simulation was conducted on the turbine and compressor. Through this simulation, the effects of parts on temperature, pressure, and speed are visually illustrated. Finally, a thrust calculation was performed.