x^3-4x-2x+3x=6x-5x

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Solution for x^3-4x-2x+3x=6x-5x equation:


Simplifying
x3 + -4x + -2x + 3x = 6x + -5x

Reorder the terms:
-4x + -2x + 3x + x3 = 6x + -5x

Combine like terms: -4x + -2x = -6x
-6x + 3x + x3 = 6x + -5x

Combine like terms: -6x + 3x = -3x
-3x + x3 = 6x + -5x

Combine like terms: 6x + -5x = 1x
-3x + x3 = 1x

Solving
-3x + x3 = 1x

Solving for variable 'x'.

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

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

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

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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