(4x-1 6)(8+x)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (4x - 16)(8 + x) = 0

This equation is a quadratic equation in factored form. To solve for x, 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.

Steps to Solve:

1. Set each factor equal to zero:

   • 4x - 16 = 0
   • 8 + x = 0

2. Solve for x in each equation:

   • 4x = 16
     • x = 4
   • x = -8

Therefore, the solutions to the equation (4x - 16)(8 + x) = 0 are x = 4 and x = -8.

Explanation:

The factored form of the equation shows us that the expression equals zero when either (4x - 16) or (8 + x) is equal to zero. We find the values of x that make each factor zero, and those are the solutions to the equation.

Verification:

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

• For x = 4:
  • (4(4) - 16)(8 + 4) = (16 - 16)(12) = 0
• For x = -8:
  • (4(-8) - 16)(8 - 8) = (-32 - 16)(0) = 0

Both solutions make the equation true, confirming that they are correct.