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(x+3)(x-4)=0

2 min read Jun 16, 2024
(x+3)(x-4)=0

Solving the Equation (x + 3)(x - 4) = 0

This equation is a quadratic equation in factored form, which makes solving for the values of x quite straightforward. Here's how to do 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.

Applying the Zero Product Property

  1. Identify the factors: In our equation, (x + 3) and (x - 4) are the factors.
  2. Set each factor equal to zero:
    • x + 3 = 0
    • x - 4 = 0
  3. Solve for x in each equation:
    • x = -3
    • x = 4

Conclusion

Therefore, the solutions to the equation (x + 3)(x - 4) = 0 are x = -3 and x = 4. These are the values of x that make the equation true.

Important Note: This method works because the equation is already factored. If the equation was not factored, we would need to use other methods like factoring, completing the square, or the quadratic formula to solve for x.

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