N(4n+1)=0

Solution for N(4n+1)=0 equation:

Simplifying
N(4n + 1) = 0

Reorder the terms:
N(1 + 4n) = 0
(1 * N + 4n * N) = 0
(1N + 4nN) = 0

Solving
1N + 4nN = 0

Solving for variable 'N'.

Move all terms containing N to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), 'N'.
N(1 + 4n) = 0

Subproblem 1
Set the factor 'N' equal to zero and attempt to solve:

Simplifying
N = 0

Solving
N = 0

Move all terms containing N to the left, all other terms to the right.

Simplifying
N = 0
Subproblem 2
Set the factor '(1 + 4n)' equal to zero and attempt to solve:

Simplifying
1 + 4n = 0

Solving
1 + 4n = 0

Move all terms containing N to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + 4n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4n = 0 + -1
4n = 0 + -1

Combine like terms: 0 + -1 = -1
4n = -1

Add '-4n' to each side of the equation.
4n + -4n = -1 + -4n

Combine like terms: 4n + -4n = 0
0 = -1 + -4n

Simplifying
0 = -1 + -4n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
N = {0}