(x-5)(x+8)=0

2 min read Jun 17, 2024

Solving the Equation (x-5)(x+8) = 0

This equation presents a simple yet powerful concept in algebra: the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Let's break down the steps to solve this equation:

1. Understanding the Factors

The equation (x-5)(x+8) = 0 is already factored for us. This means we have two factors:

(x-5)
(x+8)

2. Applying the Zero Product Property

The Zero Product Property tells us that for the product of these factors to equal zero, at least one of them must be zero. So, we set each factor equal to zero:

x - 5 = 0
x + 8 = 0

3. Solving for x

Now, we solve each equation for x:

x - 5 = 0 => x = 5
x + 8 = 0 => x = -8

4. Solution

Therefore, the solutions to the equation (x-5)(x+8) = 0 are x = 5 and x = -8.

Importance of the Zero Product Property

The Zero Product Property is a fundamental concept in algebra. It allows us to solve equations by factoring them into simpler expressions. This principle is widely used in various mathematical concepts, including quadratic equations, polynomial functions, and finding the roots of an equation.