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

2 min read Jun 16, 2024
(4x+1)(x-8)=0

Solving the Equation (4x+1)(x-8)=0

This equation is a quadratic equation in factored form. This means that it's already set up for easy solving. Here's how to solve it:

Understanding the Zero Product Property

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

In our equation, (4x+1) and (x-8) are the two factors. To make the product equal to zero, one or both of these factors must be equal to zero.

Solving for x

  1. Set each factor equal to zero:

    • 4x + 1 = 0
    • x - 8 = 0

  2. Solve for x in each equation:

    • For 4x + 1 = 0:
      • Subtract 1 from both sides: 4x = -1
      • Divide both sides by 4: x = -1/4
    • For x - 8 = 0:
      • Add 8 to both sides: x = 8

Solution

Therefore, the solutions to the equation (4x+1)(x-8)=0 are:

  • x = -1/4
  • x = 8

These are the values of x that make the equation true.

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