Solving the Equation (8x5)(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 (8x5) 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 (8x5)(2x+7)=0 are:
 x = 5/8
 x = 7/2
These two values of x make the original equation true.