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Solve for n.

35n2+38n=0
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
n=

1 answer

To solve the equation \(35n^2 + 38n = 0\), we can factor it.

First, we factor out the common term \(n\):

\[ n(35n + 38) = 0 \]

This gives us two factors to set equal to zero:

  1. \(n = 0\)
  2. \(35n + 38 = 0\)

For the second equation, we solve for \(n\):

\[ 35n + 38 = 0 \]

Subtract \(38\) from both sides:

\[ 35n = -38 \]

Now, divide by \(35\):

\[ n = -\frac{38}{35} \]

Now we have both solutions:

  1. \(n = 0\)
  2. \(n = -\frac{38}{35}\)

Thus, the solutions are:

\[ n = 0, -\frac{38}{35} \]