54x^5=6x^3

Solution for 54x^5=6x^3 equation:

Simplifying
54x5 = 6x3

Solving
54x5 = 6x3

Solving for variable 'x'.

Reorder the terms:
-6x3 + 54x5 = 6x3 + -6x3

Combine like terms: 6x3 + -6x3 = 0
-6x3 + 54x5 = 0

Factor out the Greatest Common Factor (GCF), '6x3'.
6x3(-1 + 9x2) = 0

Factor a difference between two squares.
6x3((1 + 3x)(-1 + 3x)) = 0

Ignore the factor 6.
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 '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

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

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Subproblem 3
Set the factor '(-1 + 3x)' equal to zero and attempt to solve:

Simplifying
-1 + 3x = 0

Solving
-1 + 3x = 0

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

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

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

Combine like terms: 0 + 1 = 1
3x = 1

Divide each side by '3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-0.3333333333, 0.3333333333}