(2x+4)(x-4)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (2x+4)(x-4) = 0

This equation is a quadratic equation in factored form, making it relatively straightforward to solve. Here's how we can approach it:

Understanding the Zero Product Property

The core principle we use is the Zero Product Property: if the product of two or more factors is zero, then at least one of the factors must be zero.

In our case, the factors are (2x + 4) and (x - 4). To make their product equal to zero, one or both of these factors must be zero.

Solving for x

1. Set each factor equal to zero:

   • 2x + 4 = 0
   • x - 4 = 0

2. Solve each equation for x:

   • 2x + 4 = 0

     • Subtract 4 from both sides: 2x = -4
     • Divide both sides by 2: x = -2

   • x - 4 = 0

     • Add 4 to both sides: x = 4

The Solutions

Therefore, the solutions to the equation (2x+4)(x-4) = 0 are x = -2 and x = 4.

These values of x make the equation true, as they make one or both of the factors equal to zero.