An=n(1+n)

Solution for An=n(1+n) equation:

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

Solving
nA = 1n + n2

Solving for variable 'n'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1 + A + -1n) = 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 + A + -1n)' equal to zero and attempt to solve:

Simplifying
-1 + A + -1n = 0

Solving
-1 + A + -1n = 0

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

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

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

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

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

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

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

Divide each side by '-1'.
n = -1 + A

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