(x-7)(x+4)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-7)(x+4)=0

This equation is a simple quadratic equation in factored form. Let's break down how to solve it:

Understanding 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 two factors: (x-7) and (x+4). To make their product equal to zero, at least one of these factors must be zero.

Finding the Solutions

1. Set each factor equal to zero:

   • x - 7 = 0
   • x + 4 = 0

2. Solve for x in each equation:

   • x = 7
   • x = -4

Conclusion

Therefore, the solutions to the equation (x-7)(x+4) = 0 are x = 7 and x = -4.

This means that if you substitute either 7 or -4 for x in the original equation, the equation will be true.