Solve for n.

Question

31n^2–18n=0
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

Answer 1

To solve the equation \( 31n^2 - 18n = 0 \), we can factor it.

First, we can factor out \( n \):

\[ n(31n - 18) = 0 \]

This gives us two potential solutions:

1. \( n = 0 \)
2. \( 31n - 18 = 0 \)

Now, let's solve the second equation:

\[ 31n - 18 = 0 \]

Adding 18 to both sides:

\[ 31n = 18 \]

Now, divide both sides by 31:

\[ n = \frac{18}{31} \]

Therefore, the solutions for \( n \) are:

\[ n = 0, \frac{18}{31} \]

The final answer is:

\[ 0, \frac{18}{31} \]