(x+1)3+(x-1)3=2x^3

Solution for (x+1)3+(x-1)3=2x^3 equation:

Simplifying
(x + 1) * 3 + (x + -1) * 3 = 2x3

Reorder the terms:
(1 + x) * 3 + (x + -1) * 3 = 2x3

Reorder the terms for easier multiplication:
3(1 + x) + (x + -1) * 3 = 2x3
(1 * 3 + x * 3) + (x + -1) * 3 = 2x3
(3 + 3x) + (x + -1) * 3 = 2x3

Reorder the terms:
3 + 3x + (-1 + x) * 3 = 2x3

Reorder the terms for easier multiplication:
3 + 3x + 3(-1 + x) = 2x3
3 + 3x + (-1 * 3 + x * 3) = 2x3
3 + 3x + (-3 + 3x) = 2x3

Reorder the terms:
3 + -3 + 3x + 3x = 2x3

Combine like terms: 3 + -3 = 0
0 + 3x + 3x = 2x3
3x + 3x = 2x3

Combine like terms: 3x + 3x = 6x
6x = 2x3

Solving
6x = 2x3

Solving for variable 'x'.

Combine like terms: 2x3 + -2x3 = 0
6x + -2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(3 + -1x2) = 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 '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {0, -1.732050808, 1.732050808}