S(n)=n^2

Solution for S(n)=n^2 equation:

Simplifying
S(n) = n2

Multiply S * n
nS = n2

Solving
nS = n2

Solving for variable 'n'.

Combine like terms: n2 + -1n2 = 0
nS + -1n2 = 0

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

Simplifying
S + -1n = 0

Solving
S + -1n = 0

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

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

Combine like terms: S + -1S = 0
0 + -1n = 0 + -1S
-1n = 0 + -1S
Remove the zero:
-1n = -1S

Divide each side by '-1'.
n = S

Simplifying
n = S
Solution
n = {0, S}