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

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


Simplifying
(x3 + -1x + 1) + -1(3x + 1) = 0

Reorder the terms:
(1 + -1x + x3) + -1(3x + 1) = 0

Remove parenthesis around (1 + -1x + x3)
1 + -1x + x3 + -1(3x + 1) = 0

Reorder the terms:
1 + -1x + x3 + -1(1 + 3x) = 0
1 + -1x + x3 + (1 * -1 + 3x * -1) = 0
1 + -1x + x3 + (-1 + -3x) = 0

Reorder the terms:
1 + -1 + -1x + -3x + x3 = 0

Combine like terms: 1 + -1 = 0
0 + -1x + -3x + x3 = 0
-1x + -3x + x3 = 0

Combine like terms: -1x + -3x = -4x
-4x + x3 = 0

Solving
-4x + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + x2) = 0

Factor a difference between two squares.
x((2 + x)(-2 + x)) = 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 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2

Subproblem 3
Set the factor '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

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

Simplifying
x = 2
Solution
x = {0, -2, 2}

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