Sn=2n^2-n

Solution for Sn=2n^2-n equation:

Simplifying
Sn = 2n2 + -1n

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

Solving
nS = -1n + 2n2

Solving for variable 'n'.

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

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

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

Combine like terms: 2n2 + -2n2 = 0
n + nS + -2n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(1 + S + -2n) = 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 + S + -2n)' equal to zero and attempt to solve:

Simplifying
1 + S + -2n = 0

Solving
1 + S + -2n = 0

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

Add '-1' to each side of the equation.
1 + S + -1 + -2n = 0 + -1

Reorder the terms:
1 + -1 + S + -2n = 0 + -1

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

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

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

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

Divide each side by '-2'.
n = 0.5 + 0.5S

Simplifying
n = 0.5 + 0.5S
Solution
n = {0, 0.5 + 0.5S}