x^3+7x-x=0

Solution for x^3+7x-x=0 equation:

Simplifying
x3 + 7x + -1x = 0

Reorder the terms:
7x + -1x + x3 = 0

Combine like terms: 7x + -1x = 6x
6x + x3 = 0

Solving
6x + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + x2) = 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 '(6 + x2)' equal to zero and attempt to solve:

Simplifying
6 + x2 = 0

Solving
6 + x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x2 = 0 + -6
x2 = 0 + -6

Combine like terms: 0 + -6 = -6
x2 = -6

Simplifying
x2 = -6

The solution to this equation could not be determined.

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