(x+6)(x-3)=0

3 min read Jun 17, 2024

Solving the Equation (x+6)(x-3) = 0

This equation represents a quadratic equation in factored form. To solve for the values of 'x' that satisfy the equation, we can utilize the Zero Product Property.

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.

Applying the Property to the Equation

In our equation, (x+6)(x-3) = 0, we have two factors: (x+6) and (x-3). According to the Zero Product Property, for the product to be zero, at least one of these factors must equal zero.

Therefore, we have two possible scenarios:

x + 6 = 0 Solving for x, we get: x = -6
x - 3 = 0 Solving for x, we get: x = 3

Solutions

Therefore, the solutions to the equation (x+6)(x-3) = 0 are x = -6 and x = 3.

Verification

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

For x = -6: (-6 + 6)(-6 - 3) = (0)(-9) = 0
For x = 3: (3 + 6)(3 - 3) = (9)(0) = 0

Since both solutions result in 0, we have verified that they are correct.

Conclusion

By applying the Zero Product Property, we have successfully solved the quadratic equation (x+6)(x-3) = 0, finding the solutions to be x = -6 and x = 3. This demonstrates the power of factorization in simplifying and solving equations.