(x-4)(x+2)=0 By Factorisation

2 min read Jun 17, 2024

Solving the Equation (x-4)(x+2) = 0 by Factorization

This equation is already in factored form, which makes solving it very straightforward. Here's how to solve it:

Understanding the Zero Product Property

The Zero Product Property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.

In our equation, we have two factors: (x-4) and (x+2).

Applying the Zero Product Property

To solve the equation, we set each factor equal to zero and solve for x:

Factor 1: (x - 4) = 0
- Adding 4 to both sides gives us: x = 4
Factor 2: (x + 2) = 0
- Subtracting 2 from both sides gives us: x = -2

Solution

Therefore, the solutions to the equation (x-4)(x+2) = 0 are x = 4 and x = -2.

Verification

We can verify our solutions by plugging them back into the original equation:

For x = 4:
- (4 - 4)(4 + 2) = 0 * 6 = 0
For x = -2:
- (-2 - 4)(-2 + 2) = -6 * 0 = 0

Both solutions satisfy the equation, confirming their validity.