(x+3)(x-2)(x+9)=0

2 min read Jun 16, 2024

Solving the Equation (x+3)(x-2)(x+9) = 0

This equation is a cubic equation, meaning it has a highest power of 3 for the variable x. Solving it involves finding the values of x that make the equation true.

The Zero Product Property

The key to solving this equation lies in 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.

In our equation, we have three factors: (x+3), (x-2), and (x+9). For the product to be zero, at least one of these factors must equal zero.

Finding the Solutions

Let's set each factor equal to zero and solve for x:

x + 3 = 0 Subtracting 3 from both sides, we get: x = -3
x - 2 = 0 Adding 2 to both sides, we get: x = 2
x + 9 = 0 Subtracting 9 from both sides, we get: x = -9

The Solutions

Therefore, the solutions to the equation (x+3)(x-2)(x+9) = 0 are x = -3, x = 2, and x = -9. These are the values of x that make the equation true.

Conclusion

By applying the Zero Product Property, we have successfully solved the cubic equation (x+3)(x-2)(x+9) = 0. This method allows us to find the solutions by isolating each factor and setting it equal to zero.