F(x)=1n(x^3-5x)

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Solution for F(x)=1n(x^3-5x) equation: 


Simplifying
F(x) = 1n(x3 + -5x)

Multiply F * x
xF = 1n(x3 + -5x)

Reorder the terms:
xF = 1n(-5x + x3)
xF = (-5x * 1n + x3 * 1n)
xF = (-5nx + 1nx3)

Solving
xF = -5nx + 1nx3

Solving for variable 'x'.

Reorder the terms:
5nx + -1nx3 + xF = -5nx + 1nx3 + 5nx + -1nx3

Reorder the terms:
5nx + -1nx3 + xF = -5nx + 5nx + 1nx3 + -1nx3

Combine like terms: -5nx + 5nx = 0
5nx + -1nx3 + xF = 0 + 1nx3 + -1nx3
5nx + -1nx3 + xF = 1nx3 + -1nx3

Combine like terms: 1nx3 + -1nx3 = 0
5nx + -1nx3 + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5n + -1nx2 + F) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(5n + -1nx2 + F)' equal to zero and attempt to solve:

Simplifying
5n + -1nx2 + F = 0

Reorder the terms:
F + 5n + -1nx2 = 0

Solving
F + 5n + -1nx2 = 0

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

Add '-1F' to each side of the equation.
F + 5n + -1F + -1nx2 = 0 + -1F

Reorder the terms:
F + -1F + 5n + -1nx2 = 0 + -1F

Combine like terms: F + -1F = 0
0 + 5n + -1nx2 = 0 + -1F
5n + -1nx2 = 0 + -1F
Remove the zero:
5n + -1nx2 = -1F

Add '-5n' to each side of the equation.
5n + -5n + -1nx2 = -1F + -5n

Combine like terms: 5n + -5n = 0
0 + -1nx2 = -1F + -5n
-1nx2 = -1F + -5n

Divide each side by '-1n'.
x2 = n-1F + 5

Simplifying
x2 = n-1F + 5

Reorder the terms:
x2 = 5 + n-1F

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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