(x-6)(x+9)=0

2 min read Jun 17, 2024

Solving the Equation (x - 6)(x + 9) = 0

This equation represents a quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can use 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 - 6 = 0
- x + 9 = 0
Solve for x in each equation:
- x = 6
- x = -9

Solution

Therefore, the solutions to the equation (x - 6)(x + 9) = 0 are x = 6 and x = -9.

Verifying the Solutions

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

For x = 6: (6 - 6)(6 + 9) = 0 * 15 = 0
For x = -9: (-9 - 6)(-9 + 9) = -15 * 0 = 0

As we can see, both values of x satisfy the equation.

Conclusion

The equation (x - 6)(x + 9) = 0 has two solutions: x = 6 and x = -9. These solutions represent the x-intercepts of the parabola defined by the quadratic equation.