## Solving Quadratic Equations Using the FOIL Method: (x+3)(x+4) = 0

The FOIL method is a mnemonic acronym for the steps used to multiply two binomials. It stands for **First, Outer, Inner, Last**. This method helps us to systematically expand the product of two binomials and solve quadratic equations.

Let's break down how to solve the equation **(x+3)(x+4) = 0** using the FOIL method:

### 1. Expanding the Equation

**Step 1:** Multiply the **First** terms of each binomial.

- (x) * (x) = x²

**Step 2:** Multiply the **Outer** terms of the binomials.

- (x) * (4) = 4x

**Step 3:** Multiply the **Inner** terms of the binomials.

- (3) * (x) = 3x

**Step 4:** Multiply the **Last** terms of each binomial.

- (3) * (4) = 12

Now, combine all the terms:

- x² + 4x + 3x + 12 = 0

**Step 5:** Simplify the equation by combining like terms.

- x² + 7x + 12 = 0

### 2. Solving the Quadratic Equation

The equation x² + 7x + 12 = 0 is now in standard quadratic form (ax² + bx + c = 0). We can solve this equation by factoring or by using the quadratic formula.

**Factoring Method:**

**Find two numbers that add up to 7 (the coefficient of the x term) and multiply to 12 (the constant term).**- These numbers are 3 and 4.
- Rewrite the equation as: (x + 3)(x + 4) = 0

**Zero Product Property:**

- The zero product property states that if the product of two factors is zero, then at least one of the factors must be zero.
- Therefore, either (x + 3) = 0 or (x + 4) = 0

**Solving for x:**

**x + 3 = 0**=> x = -3**x + 4 = 0**=> x = -4

### Conclusion

By using the FOIL method to expand the equation (x+3)(x+4) = 0, we were able to solve the quadratic equation and find the solutions: **x = -3** and **x = -4**.