x=Ax-Nx

Solution for x=Ax-Nx equation:

Simplifying
x = Ax + -1Nx

Solving
x = xA + -1xN

Solving for variable 'x'.

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

Add '-1xA' to each side of the equation.
x + -1xA = xA + -1xA + -1xN

Combine like terms: xA + -1xA = 0
x + -1xA = 0 + -1xN
x + -1xA = -1xN

Add 'xN' to each side of the equation.
x + -1xA + xN = -1xN + xN

Combine like terms: -1xN + xN = 0
x + -1xA + xN = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -1A + N) = 0

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

Simplifying
x = 0

Solving
x = 0

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

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

Simplifying
1 + -1A + N = 0

Solving
1 + -1A + N = 0

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

Add '-1' to each side of the equation.
1 + -1A + -1 + N = 0 + -1

Reorder the terms:
1 + -1 + -1A + N = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1A + N = 0 + -1
-1A + N = 0 + -1

Combine like terms: 0 + -1 = -1
-1A + N = -1

Add 'A' to each side of the equation.
-1A + A + N = -1 + A

Combine like terms: -1A + A = 0
0 + N = -1 + A
N = -1 + A

Add '-1N' to each side of the equation.
N + -1N = -1 + A + -1N

Combine like terms: N + -1N = 0
0 = -1 + A + -1N

Simplifying
0 = -1 + A + -1N

The solution to this equation could not be determined.

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