We are given the equation:

$-8(-8x - 6) = -2x + 7$

Step 1: Distribute the $-8$ on the left-hand side.

$-8(-8x - 6) = (-8) \cdot (-8x) + (-8) \cdot (-6)$

This simplifies to:

$64x + 48$

Now, the equation becomes:

$64x + 48 = -2x + 7$

Step 2: Move all terms involving $x$ to one side and constants to the other.

First, add $2x$ to both sides:

$64x + 2x + 48 = 7$

This simplifies to:

$66x + 48 = 7$

Next, subtract $48$ from both sides:

$66x = 7 - 48$

This simplifies to:

$66x = -41$

Step 3: Solve for $x$.

Now, divide both sides by $66$:

$x = \frac{-41}{66}$

Final Answer:

$x = \frac{-41}{66}$

Let me know if you'd like more details or have any questions!

Here are 5 related questions:

1. How do you apply the distributive property in algebraic equations?
2. Why is it important to simplify both sides of the equation before solving?
3. What happens if you forget to distribute the negative sign properly in such problems?
4. Can you solve a similar equation: $5(3x - 4) = 2x + 8$?
5. How do you check if the solution to a linear equation is correct?

Tip: Always double-check your work when distributing negative signs, as small errors can lead to incorrect solutions.