(x-7)(x+3)=0

2 min read Jun 17, 2024

Solving the Equation: (x - 7)(x + 3) = 0

This equation is a quadratic equation in factored form, which makes it particularly easy to solve. Here's how we can find the solutions:

Understanding the Zero Product Property

The Zero Product 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, (x - 7) and (x + 3) are the factors.

Finding the Solutions

Set each factor equal to zero:
- x - 7 = 0
- x + 3 = 0
Solve for x in each equation:
- x = 7
- x = -3

Therefore, the solutions to the equation (x - 7)(x + 3) = 0 are x = 7 and x = -3.

Checking our Solutions

We can check our answers by plugging them back into the original equation:

For x = 7: (7 - 7)(7 + 3) = 0 * 10 = 0. This solution works!
For x = -3: (-3 - 7)(-3 + 3) = -10 * 0 = 0. This solution also works!

Conclusion

We have successfully found the solutions to the equation (x - 7)(x + 3) = 0 using the Zero Product Property. The solutions are x = 7 and x = -3.