T(n)=2n^2+n

Solution for T(n)=2n^2+n equation:

Simplifying
T(n) = 2n2 + n

Multiply T * n
nT = 2n2 + n

Reorder the terms:
nT = n + 2n2

Solving
nT = n + 2n2

Solving for variable 'n'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1 + T + -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 + T + -2n)' equal to zero and attempt to solve:

Simplifying
-1 + T + -2n = 0

Solving
-1 + T + -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 + T + 1 + -2n = 0 + 1

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

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

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

Add '-1T' to each side of the equation.
T + -1T + -2n = 1 + -1T

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

Divide each side by '-2'.
n = -0.5 + 0.5T

Simplifying
n = -0.5 + 0.5T
Solution
n = {0, -0.5 + 0.5T}