(x+5)(x-4)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x+5)(x-4) = 0

This equation is a quadratic equation in factored form. To solve for the values of x that satisfy this 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

1. Set each factor equal to zero:

   • x + 5 = 0
   • x - 4 = 0

2. Solve each equation for x:

   • x = -5
   • x = 4

Conclusion

Therefore, the solutions to the equation (x+5)(x-4) = 0 are x = -5 and x = 4. These are the values of x that make the equation true.

Checking the Solutions

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

• For x = -5:
  • (-5 + 5)(-5 - 4) = (0)(-9) = 0
• For x = 4:
  • (4 + 5)(4 - 4) = (9)(0) = 0

Both solutions satisfy the equation, confirming our results.