x^4=-6x^3

Solution for x^4=-6x^3 equation:

Simplifying
x4 = -6x3

Solving
x4 = -6x3

Solving for variable 'x'.

Reorder the terms:
6x3 + x4 = -6x3 + 6x3

Combine like terms: -6x3 + 6x3 = 0
6x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(6 + x) = 0

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {-6}