Solve each equation. Show your reasoning.​a.  (x−8)(2x+5)=0(𝑥−8)(2𝑥+5)=0 Type the answer in the box below.x=𝑥=   or   x=𝑥=

1. Break Down the Problem

To solve the equation $(x−8)(2x+5) = 0$, we need to set each factor equal to zero and solve for $x$.

2. Relevant Concepts

If a product of two factors equals zero, then at least one of the factors must be zero. Thus, we can set up the following equations:

1. $x - 8 = 0$
2. $2x + 5 = 0$

3. Analysis and Detail

1. Solve the first equation: $x - 8 = 0 \\ x = 8$

2. Solve the second equation: $2x + 5 = 0 \\ 2x = -5 \\ x = -\frac{5}{2}$

4. Verify and Summarize

Both equations yield valid solutions for $x$. We have found two values: $x = 8$ and $x = -\frac{5}{2}$.

Final Answer

Thus, the solutions are: $x = 8 \quad \text{or} \quad x = -\frac{5}{2}$