1. We start from the original problem and aim to solve it by a different method. 2. Let's assume the original problem is solving the quadratic equation $ax^2 + bx + c = 0$ by the quadratic formula. 3. Another way is by factoring, if possible. 4. For example, if the equation is $x^2 - 5x + 6 = 0$, then we factor it as $(x - 2)(x - 3) = 0$. 5. Setting each factor equal to zero gives the solutions $x = 2$ and $x = 3$. 6. This method avoids using the quadratic formula and instead relies on factorization and the zero-product property.