6x^6=54x^4

Solution for 6x^6=54x^4 equation:

Simplifying
6x6 = 54x4

Solving
6x6 = 54x4

Solving for variable 'x'.

Reorder the terms:
-54x4 + 6x6 = 54x4 + -54x4

Combine like terms: 54x4 + -54x4 = 0
-54x4 + 6x6 = 0

Factor out the Greatest Common Factor (GCF), '6x4'.
6x4(-9 + x2) = 0

Factor a difference between two squares.
6x4((3 + x)(-3 + x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve:

Simplifying
x4 = 0

Solving
x4 = 0

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

Simplifying
x4 = 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 3
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Solution
x = {-3, 3}