(x+6)(x+2)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x+6)(x+2) = 0

This equation represents a quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can utilize 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 + 6 = 0
   • x + 2 = 0

2. Solve for x in each equation:

   • x = -6
   • x = -2

Therefore, the solutions to the equation (x+6)(x+2) = 0 are x = -6 and x = -2.

Verification

We can verify our solutions by substituting them back into the original equation:

• For x = -6:
  • (-6 + 6)(-6 + 2) = (0)(-4) = 0
• For x = -2:
  • (-2 + 6)(-2 + 2) = (4)(0) = 0

As both solutions result in 0, we have confirmed that they are indeed the correct solutions.

Conclusion

By applying the Zero Product Property, we have successfully solved the quadratic equation (x+6)(x+2) = 0 and found the solutions x = -6 and x = -2. This approach offers a straightforward and efficient method for solving equations presented in factored form.