To solve the equation $x^2 - 9x + 18 = 0$ by factoring, follow these steps:

1. Identify the quadratic equation: $x^2 - 9x + 18 = 0$.

2. Find two numbers that multiply to 18 (the constant term) and add to -9 (the coefficient of $x$).

   These numbers are $-6$ and $-3$, since: $-6 \cdot -3 = 18 \quad \text{and} \quad -6 + -3 = -9.$

3. Write the equation in factored form: $(x - 6)(x - 3) = 0$

4. Solve for $x$: Set each factor equal to zero: $x - 6 = 0 \quad \text{or} \quad x - 3 = 0$

   Solving these gives: $x = 6 \quad \text{and} \quad x = 3$

Final Solution:

The solutions are $x = 6$ and $x = 3$.

Would you like more details or have any questions?

1. How does factoring help solve quadratic equations?
2. What if the quadratic equation can't be factored easily?
3. Can this method be used for equations with coefficients other than 1?
4. What other methods are available to solve quadratics?
5. How can you verify the solutions are correct?

Tip: Always double-check by substituting the solutions back into the original equation!