(x-8)(x+6)=0

2 min read Jun 17, 2024

Solving the Equation: (x-8)(x+6) = 0

This equation presents a simple yet fundamental 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:

Step 1: Identify the Factors

We have two factors in this equation:

(x-8)
(x+6)

Step 2: Apply the Zero Product Property

For the product of these factors to equal zero, at least one of them must be zero. Therefore, we can set each factor equal to zero and solve for x:

Case 1: (x-8) = 0

Adding 8 to both sides gives us: x = 8

Case 2: (x+6) = 0

Subtracting 6 from both sides gives us: x = -6

Step 3: Solution

Therefore, the solutions to the equation (x-8)(x+6) = 0 are x = 8 and x = -6.

Conclusion

By applying the Zero Product Property, we can efficiently solve equations where the product of factors equals zero. In this specific case, we found two distinct solutions: x = 8 and x = -6.