Let's solve the equation:

\[
4(-3r + 4) = -8(-2r + 5)
\]

### Step 1: Distribute on both sides
Distribute the constants \(4\) and \(-8\) across the terms inside the parentheses.

\[
4(-3r) + 4(4) = -8(-2r) + -8(5)
\]

This simplifies to:

\[
-12r + 16 = 16r - 40
\]

### Step 2: Move all \(r\)-terms to one side
Add \(12r\) to both sides to get all \(r\)-terms on one side:

\[
16 = 28r - 40
\]

### Step 3: Move constant terms to the other side
Add \(40\) to both sides:

\[
56 = 28r
\]

### Step 4: Solve for \(r\)
Divide both sides by \(28\):

\[
r = \frac{56}{28} = 2
\]

### Final Answer:
\[
r = 2
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve linear equations with variables on both sides?
2. What happens if you end up with a false statement like \(0 = 5\) when solving an equation?
3. How can you check your solution for an equation?
4. How would you solve an equation if it contained fractions?
5. How does distributing work with negative signs?

**Tip:** Always double-check by plugging your solution back into the original equation!

Learn how to solve the linear equation 4(-3r + 4) = -8(-2r + 5) with a detailed step-by-step solution. This problem demonstrates the distributive property, moving variables, and solving for r. Suitable for students in Grades 8-10.

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