(x-4)(2x+1)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation: (x-4)(2x+1) = 0

This equation involves a product of two factors that equals zero. This is a key concept in algebra, known as the Zero Product Property. It states that if the product of two factors is zero, then at least one of the factors must be zero.

Here's how to solve the equation (x-4)(2x+1) = 0:

Applying the Zero Product Property

1. Set each factor equal to zero:

   • x - 4 = 0
   • 2x + 1 = 0

2. Solve each equation for x:

   • x - 4 = 0
     • Add 4 to both sides: x = 4
   • 2x + 1 = 0
     • Subtract 1 from both sides: 2x = -1
     • Divide both sides by 2: x = -1/2

Solutions

Therefore, the solutions to the equation (x-4)(2x+1) = 0 are:

• x = 4
• x = -1/2

These values of x make the original equation true because when substituted, they cause one or both of the factors to become zero, resulting in a product of zero.