(2x+6)(2x+8)=120

Jasonbradley

2 min read Jun 16, 2024

Solving the Equation (2x+6)(2x+8) = 120

This article will guide you through the process of solving the equation (2x+6)(2x+8) = 120.

Step 1: Expanding the Equation

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

(2x+6)(2x+8) = 4x² + 16x + 12x + 48

Simplifying the equation:

4x² + 28x + 48 = 120

Step 2: Rearranging the Equation

Next, we need to move all terms to one side of the equation to get a quadratic equation in standard form:

4x² + 28x + 48 - 120 = 0

Simplifying the equation:

4x² + 28x - 72 = 0

Step 3: Solving the Quadratic Equation

Now we have a quadratic equation in standard form (ax² + bx + c = 0). We can solve this equation using various methods, such as factoring, completing the square, or using the quadratic formula.

Let's use factoring in this case:

Divide the equation by 4: x² + 7x - 18 = 0
Factor the quadratic expression: (x+9)(x-2) = 0
Set each factor equal to zero: x + 9 = 0 or x - 2 = 0
Solve for x: x = -9 or x = 2

Solution

Therefore, the solutions to the equation (2x+6)(2x+8) = 120 are x = -9 and x = 2.