1. **State the problem:** Solve a quadratic equation by factorization method. 2. **General form:** A quadratic equation is written as $$ax^2 + bx + c = 0$$ where $a \neq 0$. 3. **Step 1: Rearrange the equation** so that all terms are on one side and zero is on the other side. 4. **Step 2: Factorize the quadratic expression** on the left side. This means expressing it as a product of two binomials, for example: $$ax^2 + bx + c = (mx + n)(px + q)$$ 5. **Step 3: Set each factor equal to zero:** $$mx + n = 0$$ $$px + q = 0$$ 6. **Step 4: Solve each linear equation:** $$x = -\frac{n}{m}$$ and $$x = -\frac{q}{p}$$ 7. **Step 5: Check your solutions** by substituting them back into the original quadratic equation to verify they satisfy it. **Important rules:** - The zero product property states if $$AB = 0$$ then either $$A = 0$$ or $$B = 0$$. - Factorization requires finding two numbers that multiply to $$ac$$ and add to $$b$$ when $a \neq 1$. **Difference from linear equations:** - Quadratic equations involve $x^2$ terms and can have two solutions. - Linear equations involve only $x$ to the first power and have one solution. This method works well when the quadratic can be factored easily into rational factors.