Tn=n(5-3n)

Solution for Tn=n(5-3n) equation:

Simplifying
Tn = n(5 + -3n)
nT = (5 * n + -3n * n)
nT = (5n + -3n2)

Solving
nT = 5n + -3n2

Solving for variable 'n'.

Reorder the terms:
-5n + nT + 3n2 = 5n + -3n2 + -5n + 3n2

Reorder the terms:
-5n + nT + 3n2 = 5n + -5n + -3n2 + 3n2

Combine like terms: 5n + -5n = 0
-5n + nT + 3n2 = 0 + -3n2 + 3n2
-5n + nT + 3n2 = -3n2 + 3n2

Combine like terms: -3n2 + 3n2 = 0
-5n + nT + 3n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5 + T + 3n) = 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 '(-5 + T + 3n)' equal to zero and attempt to solve:

Simplifying
-5 + T + 3n = 0

Solving
-5 + T + 3n = 0

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

Add '5' to each side of the equation.
-5 + T + 5 + 3n = 0 + 5

Reorder the terms:
-5 + 5 + T + 3n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + T + 3n = 0 + 5
T + 3n = 0 + 5

Combine like terms: 0 + 5 = 5
T + 3n = 5

Add '-1T' to each side of the equation.
T + -1T + 3n = 5 + -1T

Combine like terms: T + -1T = 0
0 + 3n = 5 + -1T
3n = 5 + -1T

Divide each side by '3'.
n = 1.666666667 + -0.3333333333T

Simplifying
n = 1.666666667 + -0.3333333333T
Solution
n = {0, 1.666666667 + -0.3333333333T}