1. The problem is to solve the quadratic equation $$x^2 - 5x + 6 = 0.$$\n\n2. To solve this quadratic equation, we can factor it. We look for two numbers that multiply to $6$ and add up to $-5$.\n\n3. Those numbers are $-2$ and $-3$, so we factor the equation as $$(x - 2)(x - 3) = 0.$$\n\n4. Setting each factor equal to zero gives two solutions: $$x - 2 = 0 \Rightarrow x = 2,$$ and $$x - 3 = 0 \Rightarrow x = 3.$$\n\n5. Therefore, the solutions to the equation are $$x = 2$$ and $$x = 3.$$