1. **State the problem:** Solve the quadratic equation $$x^2 - 3x + 2 = 0$$. 2. **Recall the factoring method:** To solve quadratic equations by factoring, we express the quadratic as a product of two binomials equal to zero: $$ax^2 + bx + c = 0 \implies (x - r)(x - s) = 0$$ where $r$ and $s$ are roots. 3. **Factorise the quadratic:** Find two numbers that multiply to $2$ (the constant term) and add to $-3$ (the coefficient of $x$). These numbers are $-1$ and $-2$. 4. Write the factorised form: $$x^2 - 3x + 2 = (x - 1)(x - 2)$$ 5. **Set each factor equal to zero:** $$x - 1 = 0 \quad \text{or} \quad x - 2 = 0$$ 6. **Solve each equation:** $$x = 1 \quad \text{or} \quad x = 2$$ **Final answer:** The solutions to the equation are $$x = 1$$ and $$x = 2$$.