Let's simplify the equation:
\[ 4^2 + 3 + 1 = 0. \]
Calculating \( 4^2 \):
\[ 4^2 = 16. \]
Now substituting this back into the equation:
\[ 16 + 3 + 1 = 0. \]
Now simplify the left-hand side:
\[ 16 + 3 = 19, \] \[ 19 + 1 = 20. \]
So, we have:
\[ 20 = 0. \]
This is a contradiction, which means that the equation \( 4^2 + 3 + 1 = 0 \) has no solutions.