0=x^5-2x^3-8x

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Solution for 0=x^5-2x^3-8x equation:


Simplifying
0 = x5 + -2x3 + -8x

Reorder the terms:
0 = -8x + -2x3 + x5

Solving
0 = -8x + -2x3 + x5

Solving for variable 'x'.
Remove the zero:
8x + 2x3 + -1x5 = -8x + -2x3 + x5 + 8x + 2x3 + -1x5

Reorder the terms:
8x + 2x3 + -1x5 = -8x + 8x + -2x3 + 2x3 + x5 + -1x5

Combine like terms: -8x + 8x = 0
8x + 2x3 + -1x5 = 0 + -2x3 + 2x3 + x5 + -1x5
8x + 2x3 + -1x5 = -2x3 + 2x3 + x5 + -1x5

Combine like terms: -2x3 + 2x3 = 0
8x + 2x3 + -1x5 = 0 + x5 + -1x5
8x + 2x3 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
8x + 2x3 + -1x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + 2x2 + -1x4) = 0

Factor a trinomial.
x((4 + -1x2)(2 + x2)) = 0

Factor a difference between two squares.
x(((2 + x)(2 + -1x))(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 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

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

Subproblem 4

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {0, -2, 2}

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