1. Let's create a math question about solving a quadratic equation.\n\n2. Problem: Solve the quadratic equation $$x^2 - 5x + 6 = 0$$.\n\n3. Step 1: Identify coefficients in the quadratic equation $$ax^2 + bx + c = 0$$, where $$a=1$$, $$b=-5$$, and $$c=6$$.\n\n4. Step 2: Factor the quadratic if possible. We look for two numbers that multiply to $$c = 6$$ and add to $$b = -5$$. These numbers are $$-2$$ and $$-3$$, since $$-2 \times -3 = 6$$ and $$-2 + -3 = -5$$.\n\n5. Step 3: Rewrite the quadratic as $$(x - 2)(x - 3) = 0$$.\n\n6. Step 4: Apply the zero product property, setting each factor equal to zero: $$x - 2 = 0$$ or $$x - 3 = 0$$.\n\n7. Step 5: Solve each equation: $$x = 2$$ or $$x = 3$$.\n\n8. Therefore, the solutions to the quadratic equation $$x^2 - 5x + 6 = 0$$ are $$x = 2$$ and $$x = 3$$.