216x^5-48x^3+2x=0

Solution for 216x^5-48x^3+2x=0 equation:

Simplifying
216x5 + -48x3 + 2x = 0

Reorder the terms:
2x + -48x3 + 216x5 = 0

Solving
2x + -48x3 + 216x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(1 + -24x2 + 108x4) = 0

Factor a trinomial.
2x((1 + -18x2)(1 + -6x2)) = 0

Ignore the factor 2.
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 '(1 + -18x2)' equal to zero and attempt to solve:

Simplifying
1 + -18x2 = 0

Solving
1 + -18x2 = 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 + -18x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -18x2 = 0 + -1
-18x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-18x2 = -1

Divide each side by '-18'.
x2 = 0.05555555556

Simplifying
x2 = 0.05555555556

Take the square root of each side:
x = {-0.23570226, 0.23570226}
Subproblem 3
Set the factor '(1 + -6x2)' equal to zero and attempt to solve:

Simplifying
1 + -6x2 = 0

Solving
1 + -6x2 = 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 + -6x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6x2 = 0 + -1
-6x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-6x2 = -1

Divide each side by '-6'.
x2 = 0.1666666667

Simplifying
x2 = 0.1666666667

Take the square root of each side:
x = {-0.408248291, 0.408248291}
Solution
x = {0, -0.23570226, 0.23570226, -0.408248291, 0.408248291}