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

2 min read Jun 17, 2024

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

This equation is a simple quadratic equation that can be solved using 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 Zero Product Property

Identify the factors: In the equation (x-4)(x+2) = 0, we have two factors: (x-4) and (x+2).
Set each factor to zero: We need to find the values of x that make each factor equal to zero.
- x - 4 = 0
- x + 2 = 0
Solve for x:
- x = 4
- x = -2

Solutions

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

Checking the Solutions

We can check 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

Since both solutions result in zero, we have verified that they are correct.

Conclusion

The equation (x-4)(x+2) = 0 has two solutions: x = 4 and x = -2. These solutions can be easily found by applying the Zero Product Property.