F(k)=3k*u(k-2)

Solution for F(k)=3k*u(k-2) equation:

Simplifying
F(k) = 3k * u(k + -2)

Multiply F * k
kF = 3k * u(k + -2)

Reorder the terms:
kF = 3k * u(-2 + k)

Multiply k * u
kF = 3ku(-2 + k)
kF = (-2 * 3ku + k * 3ku)
kF = (-6ku + 3k2u)

Solving
kF = -6ku + 3k2u

Solving for variable 'k'.

Reorder the terms:
kF + 6ku + -3k2u = -6ku + 6ku + 3k2u + -3k2u

Combine like terms: -6ku + 6ku = 0
kF + 6ku + -3k2u = 0 + 3k2u + -3k2u
kF + 6ku + -3k2u = 3k2u + -3k2u

Combine like terms: 3k2u + -3k2u = 0
kF + 6ku + -3k2u = 0

Factor out the Greatest Common Factor (GCF), 'k'.
k(F + 6u + -3ku) = 0

Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(F + 6u + -3ku)' equal to zero and attempt to solve:

Simplifying
F + 6u + -3ku = 0

Reorder the terms:
F + -3ku + 6u = 0

Solving
F + -3ku + 6u = 0

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

Add '-1F' to each side of the equation.
F + -3ku + -1F + 6u = 0 + -1F

Reorder the terms:
F + -1F + -3ku + 6u = 0 + -1F

Combine like terms: F + -1F = 0
0 + -3ku + 6u = 0 + -1F
-3ku + 6u = 0 + -1F
Remove the zero:
-3ku + 6u = -1F

Add '-6u' to each side of the equation.
-3ku + 6u + -6u = -1F + -6u

Combine like terms: 6u + -6u = 0
-3ku + 0 = -1F + -6u
-3ku = -1F + -6u

Divide each side by '-3u'.
k = 0.3333333333u-1F + 2

Simplifying
k = 0.3333333333u-1F + 2

Reorder the terms:
k = 2 + 0.3333333333u-1F
Solution
k = {0, 2 + 0.3333333333u-1F}