The purchase and sale of agricultural tractors are strongly influenced by supply and demand dynamics, making accurate forecasting essential for optimising these transactions. This study presents a novel hybrid methodology that integrates Long Short-Term Memory (LSTM) neural networks with Teaching-Learning-Based Optimisation (TLBO) to enhance decision-making in tractor sales forecasting. The proposed approach leverages TLBO to dynamically optimise critical LSTM hyperparameters, such as the number of layers, neurons, and learning rate, thereby reducing manual intervention and improving model adaptability. Using time series data from January 1961 to December 2020, the hybrid model was trained and evaluated, achieving significant improvements in predictive accuracy compared to standalone LSTM models. The results highlight the potential of this methodology for complex forecasting tasks, providing a scalable framework for decision-making in agricultural markets. Additionally, the versatility of the proposed approach makes it applicable to various domains requiring precise time series predictions.