Solve the following equation for BB. Be sure to take into account whether a letter is capitalized or not.
g, B, minus, N, cubed, B, equals, d
gB−N 
3
 B=
d

To solve the equation

\[
gB - N^3 B = d
\]

for \( B \), let's go through it step-by-step.

### Step 1: Factor out \( B \)
Rewrite the equation by factoring out \( B \) from the left side:

\[
B(g - N^3) = d
\]

### Step 2: Divide by \( (g - N^3) \) 
Assuming \( g - N^3 \neq 0 \), divide both sides by \( g - N^3 \) to isolate \( B \):

\[
B = \frac{d}{g - N^3}
\]

### Solution
Thus, the solution for \( B \) is:

\[
B = \frac{d}{g - N^3}
\]

If \( g - N^3 = 0 \), then the equation has no solution for \( B \) because it would involve division by zero.

Would you like further details or have any questions?

Here are five related questions you may find helpful:
1. What happens if \( g = N^3 \) in this type of equation?
2. How can you verify solutions when variables are substituted with numbers?
3. How would you solve if another term were added to the left side?
4. Can we use similar factoring techniques in quadratic equations?
5. How does capitalization affect solving equations in general?

**Tip:** Always check for cases where division by zero might occur to avoid undefined solutions.

Solve the following equation for B. Be sure to take into account whether a letter is capitalized or not.
gB - N^3 B = d

Discover how to solve the algebraic equation gB - N^3 B = d for B with a step-by-step solution. This solution covers key algebra concepts like factoring and handling cases with division by zero, making it suitable for students in Grades 9-11.

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