Let's solve the equation step by step:
The given equation is:
\[ 3(3n + 5) + 1 = 2(n - 20) \]
First, distribute the numbers outside the parentheses:
\[ 9n + 15 + 1 = 2n - 40 \]
Now combine like terms on the left side:
\[ 9n + 16 = 2n - 40 \]
Next, let's isolate the \( n \) terms by subtracting \( 2n \) from both sides:
\[ 9n - 2n + 16 = -40 \] \[ 7n + 16 = -40 \]
Now, subtract 16 from both sides:
\[ 7n = -40 - 16 \] \[ 7n = -56 \]
Finally, divide both sides by 7:
\[ n = -\frac{56}{7} \] \[ n = -8 \]
So, the solution is:
\[ n = -8 \]