(x+2)(x-6)=0

2 min read Jun 16, 2024

Solving the Equation (x+2)(x-6) = 0

This equation represents a simple quadratic equation in factored form. Let's break down how to solve it:

Understanding the Zero Product Property

The key to solving this equation lies in 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.

Applying the Property

In our equation, (x+2) and (x-6) are the two factors. Therefore, for the product to be zero, either:

(x+2) = 0 or
(x-6) = 0

Solving for x

Now we have two simple linear equations to solve:

For (x+2) = 0:
- Subtract 2 from both sides:
  - x = -2
For (x-6) = 0:
- Add 6 to both sides:
  - x = 6

Solutions

Therefore, the solutions to the equation (x+2)(x-6) = 0 are x = -2 and x = 6.

Verification

We can verify these solutions by substituting them back into the original equation:

For x = -2:
- (-2 + 2)(-2 - 6) = (0)(-8) = 0
For x = 6:
- (6 + 2)(6 - 6) = (8)(0) = 0

Since both substitutions result in 0, we have confirmed that our solutions are correct.