(8x-5)(2x+7)=0

Jasonbradley

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Jun 16, 2024

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Solving the Equation (8x-5)(2x+7)=0

This equation involves a product of two binomials that equals zero. To solve for x, we can apply the Zero Product Property:

If the product of two or more factors is zero, then at least one of the factors must be zero.

Let's break down the steps:

1. Set each factor equal to zero

Since the product of (8x-5) and (2x+7) equals zero, either one or both of these factors must be equal to zero. Therefore, we set up two separate equations:

• 8x - 5 = 0
• 2x + 7 = 0

2. Solve for x in each equation

• Equation 1: 8x - 5 = 0

  • Add 5 to both sides: 8x = 5
  • Divide both sides by 8: x = 5/8

• Equation 2: 2x + 7 = 0

  • Subtract 7 from both sides: 2x = -7
  • Divide both sides by 2: x = -7/2

3. The solutions

Therefore, the solutions to the equation (8x-5)(2x+7)=0 are:

• x = 5/8
• x = -7/2

These two values of x make the original equation true.