To solve the equation \(-5(-2 - 8m) = 10 - 5m\), let's start by expanding and simplifying both sides of the equation.

### Step 1: Distribute the \(-5\) on the left side
\[
-5(-2 - 8m) = (-5) \cdot (-2) + (-5) \cdot (-8m)
\]

Calculating each term:
\[
-5 \cdot (-2) = 10, \quad \text{and} \quad -5 \cdot (-8m) = 40m
\]

So, the left side becomes:
\[
10 + 40m
\]

Thus, the equation is now:
\[
10 + 40m = 10 - 5m
\]

### Step 2: Combine like terms
Let's subtract 10 from both sides to simplify further:
\[
10 + 40m - 10 = 10 - 5m - 10
\]

This simplifies to:
\[
40m = -5m
\]

### Step 3: Solve for \(m\)
Add \(5m\) to both sides to isolate \(m\):
\[
40m + 5m = -5m + 5m
\]

This gives:
\[
45m = 0
\]

Now, divide by 45 to solve for \(m\):
\[
m = \frac{0}{45} = 0
\]

### Solution
The value of \(m\) is:
\[
\boxed{m = 0}
\]

Would you like further details on any step, or have any other questions?

### Related Questions to Explore:
1. What would be the solution if the equation was \(-5(-2 - 8m) = 15 - 5m\)?
2. How do you solve a linear equation with fractions, like \(\frac{2}{3}x - \frac{1}{4} = 5\)?
3. What happens if both sides of a linear equation have the same variable terms, like \(5x + 2 = 5x + 8\)?
4. How do you solve an equation involving parentheses, like \(3(x + 4) - 2(x - 5) = 10\)?
5. Can a linear equation have more than one solution? If so, under what conditions?

### Tip:
When solving equations, always start by simplifying both sides as much as possible, combining like terms, and then isolating the variable step-by-step.

Learn how to solve the linear equation -5(-2 - 8m) = 10 - 5m using the distributive property and combining like terms. This problem is ideal for students in Grades 8-10, covering essential algebraic techniques.

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