1. The problem is to solve the equation $x^2 - 5x + 6 = 0$ for $x$. 2. We use the quadratic equation formula or factorization method. Here, factorization is simpler. 3. Factor the quadratic: $x^2 - 5x + 6 = (x - 2)(x - 3)$. 4. Set each factor equal to zero: $x - 2 = 0$ or $x - 3 = 0$. 5. Solve each equation: $x = 2$ or $x = 3$. 6. Therefore, the solutions to the equation are $x = 2$ and $x = 3$.