An=n(2-n)

Solution for An=n(2-n) equation:

Simplifying
An = n(2 + -1n)
nA = (2 * n + -1n * n)
nA = (2n + -1n2)

Solving
nA = 2n + -1n2

Solving for variable 'n'.

Reorder the terms:
-2n + nA + n2 = 2n + -1n2 + -2n + n2

Reorder the terms:
-2n + nA + n2 = 2n + -2n + -1n2 + n2

Combine like terms: 2n + -2n = 0
-2n + nA + n2 = 0 + -1n2 + n2
-2n + nA + n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
-2n + nA + n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-2 + A + n) = 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 '(-2 + A + n)' equal to zero and attempt to solve:

Simplifying
-2 + A + n = 0

Solving
-2 + A + n = 0

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

Add '2' to each side of the equation.
-2 + A + 2 + n = 0 + 2

Reorder the terms:
-2 + 2 + A + n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + A + n = 0 + 2
A + n = 0 + 2

Combine like terms: 0 + 2 = 2
A + n = 2

Add '-1A' to each side of the equation.
A + -1A + n = 2 + -1A

Combine like terms: A + -1A = 0
0 + n = 2 + -1A
n = 2 + -1A

Simplifying
n = 2 + -1A
Solution
n = {0, 2 + -1A}