Teachers’ career planning is one of the areas of focus in education management. This paper uses hyperplane and Lagrange optimization to classify samples and then constructs a prediction model of teachers’ career plans. Based on this, we analyzed the factors that influence teachers’ career satisfaction using both factor analysis and regression analysis techniques. The results indicated that an increase of 1 unit in career exploration, interpersonal relationships, ability improvement, and self-awareness led to a corresponding increase in teachers’ career satisfaction of 0.688, 0.242, 0.153, and 0.121 units, respectively. Therefore, this paper proposes to optimize teachers’ career development paths in terms of self-awareness of professional development, interpersonal communication, faculty management optimization, and full use of prediction models.