x-0.5x^3=0

Solution for x-0.5x^3=0 equation:

Simplifying
x + -0.5x3 = 0

Solving
x + -0.5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -0.5x2) = 0

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 + -0.5x2)' equal to zero and attempt to solve:

Simplifying
1 + -0.5x2 = 0

Solving
1 + -0.5x2 = 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 + -0.5x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -0.5x2 = 0 + -1
-0.5x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-0.5x2 = -1

Divide each side by '-0.5'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Solution
x = {0, -1.414213562, 1.414213562}