Factoring is a powerful method to solve quadratic equations. It involves breaking down a quadratic expression into its factors, which allows us to find the solutions of the equation. Let's go through the step-by-step process of factoring quadratic expressions and solving equations using the factored form.

Step 1: Rewrite the equation in the standard form ax^2 + bx + c = 0, where a is not equal to zero.

Step 2: Identify two numbers, let's call them p and q, such that their sum is equal to b (coefficient of x) and their product is equal to c (constant term). Example: if the equation is x^2 + 5x + 6 = 0, then p + q = 5 and p * q = 6.

Step 3: Rewrite the middle term (bx) of the quadratic expression using p and q. In the above example, we rewrite 5x as px + qx, where p = 2 and q = 3. So, the equation becomes x^2 + 2x + 3x + 6 = 0.

Step 4: Group the terms and factor by grouping. In our example, we group the first two terms and the last two terms: (x^2 + 2x) + (3x + 6) = 0.

Step 5: Factor out the common terms from each group. We get x(x + 2) + 3(x + 2) = 0.

Step 6: Combine the factored terms and set each factor equal to zero. Here, we have (x + 2)(x + 3) = 0.

Step 7: Solve each equation obtained in the previous step: x + 2 = 0 or x + 3 = 0. Solving these equations gives us the solutions x = -2 and x = -3.

By following these steps, you can solve quadratic equations by factoring. It's a valuable technique that can be used when the quadratic expression can be easily factored. Keep practicing, and you'll master this method in no time!