Any digital logic circuit could be represented as a mathematical model, and a number of equations will be produced representing the different states of the system. Usually these equations are nonlinear, and by collecting them will have a system of nonlinear equations. The Bluetooth E0 is one of the stream cipher encryption algorithm which used in the Bluetooth wireless connection technology. An attack will be used against the E0 and cryptanalys it using the idea of solving the system of equations epresenting the system performance.The way used to solve the system of equations called the linearization, so that this type of attack is called the linearization attack. The linearization attack depend on solving the system of nonlinear equations after converting it to a system of linear equation or equations using one of the linearization numerical methods. Also after converting the system to a mathematical model, and linearizing it there is a problem for solving this equation, in our problem we use the Genetic Algorithm to solve this problem as an Intelligent random search.