F(n)=3n^2+4n

Solution for F(n)=3n^2+4n equation:

Simplifying
F(n) = 3n2 + 4n

Multiply F * n
nF = 3n2 + 4n

Reorder the terms:
nF = 4n + 3n2

Solving
nF = 4n + 3n2

Solving for variable 'n'.

Reorder the terms:
-4n + nF + -3n2 = 4n + 3n2 + -4n + -3n2

Reorder the terms:
-4n + nF + -3n2 = 4n + -4n + 3n2 + -3n2

Combine like terms: 4n + -4n = 0
-4n + nF + -3n2 = 0 + 3n2 + -3n2
-4n + nF + -3n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
-4n + nF + -3n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-4 + F + -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 '(-4 + F + -3n)' equal to zero and attempt to solve:

Simplifying
-4 + F + -3n = 0

Solving
-4 + F + -3n = 0

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

Add '4' to each side of the equation.
-4 + F + 4 + -3n = 0 + 4

Reorder the terms:
-4 + 4 + F + -3n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + F + -3n = 0 + 4
F + -3n = 0 + 4

Combine like terms: 0 + 4 = 4
F + -3n = 4

Add '-1F' to each side of the equation.
F + -1F + -3n = 4 + -1F

Combine like terms: F + -1F = 0
0 + -3n = 4 + -1F
-3n = 4 + -1F

Divide each side by '-3'.
n = -1.333333333 + 0.3333333333F

Simplifying
n = -1.333333333 + 0.3333333333F
Solution
n = {0, -1.333333333 + 0.3333333333F}