The expression you provided is:

$-\frac{2}{3}c + \frac{2}{5} \left(\frac{5}{6}c - 15\right)$

Let's simplify it step by step.

Step 1: Distribute $\frac{2}{5}$ in the parentheses

We need to distribute $\frac{2}{5}$ across both terms inside the parentheses:

$-\frac{2}{3}c + \frac{2}{5} \cdot \frac{5}{6}c - \frac{2}{5} \cdot 15$

Step 2: Simplify each term

1. For $\frac{2}{5} \cdot \frac{5}{6}c$: $\frac{2 \cdot 5}{5 \cdot 6}c = \frac{10}{30}c = \frac{1}{3}c$

2. For $-\frac{2}{5} \cdot 15$: $-\frac{2 \cdot 15}{5} = -\frac{30}{5} = -6$

Step 3: Substitute back into the expression

Now we have:

$-\frac{2}{3}c + \frac{1}{3}c - 6$

Step 4: Combine like terms

Combine $-\frac{2}{3}c$ and $\frac{1}{3}c$:

$-\frac{2}{3}c + \frac{1}{3}c = -\frac{1}{3}c$

So the simplified expression is:

$-\frac{1}{3}c - 6$

Final Answer

$-\frac{1}{3}c - 6$

Would you like further details or have any questions?

Here are five related questions to deepen your understanding:

1. How do you distribute a fraction over a variable expression?
2. What is the process of combining like terms with fractions?
3. How would the process change if there were multiple variables in the expression?
4. What happens if the terms inside the parentheses contain addition instead of subtraction?
5. How do you handle similar expressions if they include exponents?

Tip: When simplifying expressions, always distribute first, then combine like terms to reduce the expression step-by-step.