0=30x-60x^3

Solution for 0=30x-60x^3 equation:

Simplifying
0 = 30x + -60x3

Solving
0 = 30x + -60x3

Solving for variable 'x'.
Remove the zero:
-30x + 60x3 = 30x + -60x3 + -30x + 60x3

Reorder the terms:
-30x + 60x3 = 30x + -30x + -60x3 + 60x3

Combine like terms: 30x + -30x = 0
-30x + 60x3 = 0 + -60x3 + 60x3
-30x + 60x3 = -60x3 + 60x3

Combine like terms: -60x3 + 60x3 = 0
-30x + 60x3 = 0

Factor out the Greatest Common Factor (GCF), '30x'.
30x(-1 + 2x2) = 0

Ignore the factor 30.
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 + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + 2x2 = 0

Solving
-1 + 2x2 = 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 + 2x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x2 = 0 + 1
2x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2x2 = 1

Divide each side by '2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Solution
x = {0, -0.707106781, 0.707106781}