x^5-6x^2=0

Solution for x^5-6x^2=0 equation:

Simplifying
x5 + -6x2 = 0

Reorder the terms:
-6x2 + x5 = 0

Solving
-6x2 + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-6 + x3) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(-6 + x3)' equal to zero and attempt to solve:

Simplifying
-6 + x3 = 0

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

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

Combine like terms: 0 + 6 = 6
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.
Solution
x = {0}