(x-4)(x+6)=0

2 min read Jun 17, 2024

Solving the Equation (x-4)(x+6) = 0

This equation is a simple quadratic equation in factored form. To solve for x, we can utilize 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

Set each factor equal to zero:
- x - 4 = 0
- x + 6 = 0
Solve each equation for x:
- x = 4
- x = -6

Solutions

Therefore, the solutions to the equation (x-4)(x+6) = 0 are x = 4 and x = -6.

Verifying the Solutions

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

For x = 4: (4 - 4)(4 + 6) = 0 * 10 = 0. The equation holds true.
For x = -6: (-6 - 4)(-6 + 6) = -10 * 0 = 0. The equation holds true.

Conclusion

We have successfully solved the equation (x-4)(x+6) = 0 using the Zero Product Property, obtaining the solutions x = 4 and x = -6. These solutions are the values of x that make the equation true.