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Let's solve the equation step by step.

Given equation:

\[
-1.2(10 - 5c) = -14c - 52
\]

### Step 1: Distribute the \(-1.2\) on the left-hand side.

\[
-1.2 \times 10 + (-1.2) \times (-5c) = -12 + 6c
\]

So, the equation becomes:

\[
-12 + 6c = -14c - 52
\]

### Step 2: Move the terms involving \(c\) to one side and the constants to the other side.

Add \(14c\) to both sides:

\[
6c + 14c - 12 = -52
\]

Simplifying:

\[
20c - 12 = -52
\]

### Step 3: Isolate the \(c\) term.

Add 12 to both sides:

\[
20c = -40
\]

### Step 4: Solve for \(c\).

Divide both sides by 20:

\[
c = \frac{-40}{20} = -2
\]

So, the solution is \(c = -2\).

Do you want further details or have any questions? 

Here are some related questions:
1. How do you verify the solution to a linear equation?
2. What is the significance of distributing in solving equations?
3. How can equations be solved when fractions are involved?
4. What are the common mistakes to avoid when solving linear equations?
5. How does the solution of an equation change if you multiply both sides by a negative number?

**Tip:** Always double-check your work by substituting the solution back into the original equation.

Step-by-step solution for the linear equation -1.2(10 - 5c) = -14c - 52. This problem covers key algebraic concepts like distribution and isolating variables. Suitable for students in Grades 7-9.

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