x^3-3x+x=0

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


Simplifying
x3 + -3x + x = 0

Reorder the terms:
-3x + x + x3 = 0

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

Solving
-2x + x3 = 0

Solving for variable 'x'.

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

Simplifying
-2 + x2 = 0

Solving
-2 + x2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + x2 = 0 + 2

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

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

Simplifying
x2 = 2

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

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