1. Let's create a question involving solving a quadratic equation. Problem: Solve for $x$ in the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. To solve this, we can factor the quadratic. We look for two numbers that multiply to $6$ and add to $-5$. These numbers are $-2$ and $-3$. 3. So we write: $$x^2 - 5x + 6 = (x - 2)(x - 3) = 0$$ 4. Using the Zero Product Property, set each factor equal to zero: $$x - 2 = 0$$ or $$x - 3 = 0$$ 5. Solving each, we get: $$x = 2$$ or $$x = 3$$ Thus, the solutions to the equation are $x = 2$ and $x = 3$. This completes the problem.