(x-3)(x+7)-(x-9)(x+9)=24

Jasonbradley

2 min read

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Jun 17, 2024

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Solving the Equation (x-3)(x+7)-(x-9)(x+9)=24

This article will guide you through the steps to solve the given equation: (x-3)(x+7)-(x-9)(x+9)=24.

Step 1: Expand the Products

We start by expanding the products using the distributive property or the FOIL method:

• (x-3)(x+7) = x² + 4x - 21
• (x-9)(x+9) = x² - 81

Now, the equation becomes:

(x² + 4x - 21) - (x² - 81) = 24

Step 2: Simplify the Equation

Simplify the equation by combining like terms:

• x² + 4x - 21 - x² + 81 = 24
• 4x + 60 = 24

Step 3: Isolate the Variable

Subtract 60 from both sides of the equation to isolate the term containing the variable:

• 4x + 60 - 60 = 24 - 60
• 4x = -36

Step 4: Solve for x

Divide both sides of the equation by 4 to solve for x:

• 4x / 4 = -36 / 4
• x = -9

Solution

Therefore, the solution to the equation (x-3)(x+7)-(x-9)(x+9)=24 is x = -9.