The given equation is:

\[
d = 5t^3 - 2
\]

We need to make \( t \) the subject of the equation. Follow these steps:

### Step 1: Isolate the term containing \( t \)
Add 2 to both sides to get rid of the -2 on the right-hand side:

\[
d + 2 = 5t^3
\]

### Step 2: Divide both sides by 5
To isolate \( t^3 \), divide both sides of the equation by 5:

\[
\frac{d + 2}{5} = t^3
\]

### Step 3: Take the cube root
Now, take the cube root of both sides to solve for \( t \):

\[
t = \sqrt[3]{\frac{d + 2}{5}}
\]

Thus, the equation for \( t \) in terms of \( d \) is:

\[
t = \sqrt[3]{\frac{d + 2}{5}}
\]

Do you have any questions or want further details on this process? 

Here are 5 related questions for further exploration:
1. What is the cube root of a negative number?
2. How do you solve \( t^n = x \) for higher powers \( n \)?
3. Can you solve \( d = 5t^2 - 2 \) for \( t \)?
4. How would you find the derivative of \( d = 5t^3 - 2 \)?
5. What are some practical applications of solving cubic equations?

**Tip:** When isolating variables, always reverse the operations performed on them step by step.

Learn how to rearrange and solve for t in the cubic equation d = 5t^3 - 2 with step-by-step guidance. This tutorial covers important algebraic concepts, including inverse operations and cube roots, ideal for students in Grades 10-12.

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