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The problem provided is the equation:

\[
3 \left( x^3 + 4 \right) = -15
\]

Let's solve it step-by-step:

1. Start by dividing both sides by 3:

\[
x^3 + 4 = \frac{-15}{3}
\]

\[
x^3 + 4 = -5
\]

2. Now, subtract 4 from both sides:

\[
x^3 = -5 - 4
\]

\[
x^3 = -9
\]

3. To find \(x\), take the cube root of both sides:

\[
x = \sqrt[3]{-9}
\]

This gives us \(x = -\sqrt[3]{9}\). Hence, the correct answer is:

**C. \(\sqrt[3]{-9}\)**.

Would you like more details on any steps or have questions? 

Here are 5 related questions for practice:
1. What is the cube root of \( -27 \)?
2. Solve \( x^3 + 6 = 2 \).
3. How do you simplify \( \sqrt[3]{64} \)?
4. What is the solution to \( 2x^3 + 5 = 13 \)?
5. Explain why \( \sqrt[3]{-8} \) is a real number, but \( \sqrt{-8} \) is not.

**Tip:** Remember, cube roots can yield negative real numbers, unlike square roots.

What is the solution of the equation 3(x^3 + 4) = -15?

Learn how to solve the cubic equation 3(x^3 + 4) = -15 with a step-by-step explanation. This problem involves key algebraic concepts like cube roots and simplification. Suitable for high school students (Grades 9-12).

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