(x+2)(x-6) 0

Jasonbradley

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Jun 16, 2024

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

This equation is a quadratic equation in factored form. To find the solutions, we 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 + 2 = 0
   • x - 6 = 0

2. Solve for x in each equation:

   • x = -2
   • x = 6

Solutions

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

Verification

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

• For x = -2: (-2 + 2)(-2 - 6) = (0)(-8) = 0
• For x = 6: (6 + 2)(6 - 6) = (8)(0) = 0

Both solutions satisfy the equation, confirming that they are correct.