## Solving the Quadratic Equation: (x+2)(x-4) = 72

This article will guide you through the steps of solving the quadratic equation (x+2)(x-4) = 72. We'll break down the process and demonstrate how to find the solutions for *x*.

### Expanding the Equation

First, we need to expand the left side of the equation by multiplying the binomials:

(x+2)(x-4) = x² - 2x - 8

Now our equation becomes:

x² - 2x - 8 = 72

### Rearranging into Standard Form

To solve for *x*, we need to rearrange the equation into standard quadratic form, which is:

ax² + bx + c = 0

Subtracting 72 from both sides of our equation gives us:

x² - 2x - 80 = 0

### Solving the Quadratic Equation

Now we have a quadratic equation in standard form. There are a few ways to solve this:

**1. Factoring:**

- Find two numbers that multiply to -80 and add up to -2. These numbers are -12 and 6.
- Rewrite the equation as: (x-12)(x+6) = 0
- Set each factor equal to zero and solve for
*x*:- x - 12 = 0 => x = 12
- x + 6 = 0 => x = -6

**2. Quadratic Formula:**

The quadratic formula is a general solution for any quadratic equation in standard form:

x = (-b ± √(b² - 4ac)) / 2a

- In our equation, a = 1, b = -2, and c = -80.
- Substitute these values into the quadratic formula and simplify to find the solutions for
*x*.

**3. Completing the Square:**

This method involves manipulating the equation to create a perfect square trinomial. We can then take the square root of both sides to solve for *x*.

### Solutions

No matter which method you choose, you'll find the two solutions for the equation (x+2)(x-4) = 72 are:

**x = 12** and **x = -6**