2(1-x^2)x-x=

Solution for 2(1-x^2)x-x= equation:

Simplifying
2(1 + -1x2) * x + -1x = 0

Reorder the terms for easier multiplication:
2x(1 + -1x2) + -1x = 0
(1 * 2x + -1x2 * 2x) + -1x = 0
(2x + -2x3) + -1x = 0

Reorder the terms:
2x + -1x + -2x3 = 0

Combine like terms: 2x + -1x = 1x
1x + -2x3 = 0

Solving
1x + -2x3 = 0

Solving for variable 'x'.

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