1. The problem is to solve the equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic equation formula or factorization method. Here, factorization is simpler. 3. Factor the quadratic expression: $$x^2 - 5x + 6 = (x - 2)(x - 3)$$ 4. Set each factor equal to zero: $$x - 2 = 0 \quad \Rightarrow \quad x = 2$$ $$x - 3 = 0 \quad \Rightarrow \quad x = 3$$ 5. The solutions to the equation are $x = 2$ and $x = 3$. These are the values of $x$ that satisfy the original equation.