Quadratic equations can be solved by factoring when they can be expressed as the product of two binomials. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. To solve the equation by factoring, we need to find two numbers whose product is equal to ac (the product of the coefficients of x^2 and the constant term) and whose sum is equal to b (the coefficient of x). Let's take an example to understand this better:

Example: Solve the quadratic equation x^2 + 5x + 6 = 0

To solve this equation by factoring, we need to find two numbers whose product is 6 and whose sum is 5. The numbers that satisfy these conditions are 2 and 3. Therefore, we can rewrite the equation as (x + 2)(x + 3) = 0. Setting each factor equal to zero, we get x + 2 = 0 and x + 3 = 0. Solving these equations gives us the solutions x = -2 and x = -3.

Factoring quadratic equations can sometimes be challenging, especially when the coefficients are large or when the equation cannot be easily factored. In such cases, we can use alternative methods like the quadratic formula.