(x+3)(x-8)=60

2 min read Jun 16, 2024

Solving the Equation (x+3)(x-8) = 60

This article will guide you through solving the equation (x+3)(x-8) = 60. We'll explore the steps involved in finding the solutions for x.

1. Expanding the Equation

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

(x+3)(x-8) = x² - 8x + 3x - 24

Simplifying the equation, we get:

x² - 5x - 24 = 60

2. Transforming into a Quadratic Equation

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

x² - 5x - 24 - 60 = 0

This simplifies to:

x² - 5x - 84 = 0

3. Factoring the Quadratic Equation

Now, we can factor the quadratic equation to find the solutions for x. We need to find two numbers that add up to -5 (the coefficient of the x term) and multiply to -84 (the constant term).

The numbers -12 and 7 satisfy these conditions:

(-12) + 7 = -5 (-12) * 7 = -84

Therefore, we can factor the quadratic equation as:

(x - 12)(x + 7) = 0

4. Solving for x

For the product of two terms to be zero, at least one of the terms must be zero. So, we have two possible solutions:

x - 12 = 0 This gives us x = 12
x + 7 = 0 This gives us x = -7

Conclusion

The solutions to the equation (x+3)(x-8) = 60 are x = 12 and x = -7.