x(x^6+3x^3-18)=0

Solution for x(x^6+3x^3-18)=0 equation:

Simplifying
x(x6 + 3x3 + -18) = 0

Reorder the terms:
x(-18 + 3x3 + x6) = 0
(-18 * x + 3x3 * x + x6 * x) = 0
(-18x + 3x4 + x7) = 0

Solving
-18x + 3x4 + x7 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-18 + 3x3 + x6) = 0

Factor a trinomial.
x((-6 + -1x3)(3 + -1x3)) = 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 + -1x3)' equal to zero and attempt to solve:

Simplifying
-6 + -1x3 = 0

Solving
-6 + -1x3 = 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 + -1x3 = 0 + 6

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

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

Divide each side by '-1'.
x3 = -6

Simplifying
x3 = -6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(3 + -1x3)' equal to zero and attempt to solve:

Simplifying
3 + -1x3 = 0

Solving
3 + -1x3 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x3 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x3 = 0 + -3
-1x3 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x3 = -3

Divide each side by '-1'.
x3 = 3

Simplifying
x3 = 3

The solution to this equation could not be determined.

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