(-5)(x)=x^3-x

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Solution for (-5)(x)=x^3-x equation:


Simplifying
(-5)(x) = x3 + -1x

Reorder the terms:
-5x = -1x + x3

Solving
-5x = -1x + x3

Solving for variable 'x'.

Combine like terms: -5x + x = -4x
-4x + -1x3 = -1x + x3 + x + -1x3

Reorder the terms:
-4x + -1x3 = -1x + x + x3 + -1x3

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

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

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(4 + x2) = 0

Ignore the factor -1.

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 '(4 + x2)' equal to zero and attempt to solve: Simplifying 4 + x2 = 0 Solving 4 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 0 + -4 x2 = 0 + -4 Combine like terms: 0 + -4 = -4 x2 = -4 Simplifying x2 = -4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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