2x^5=12x^3-16x

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Solution for 2x^5=12x^3-16x equation:


Simplifying
2x5 = 12x3 + -16x

Reorder the terms:
2x5 = -16x + 12x3

Solving
2x5 = -16x + 12x3

Solving for variable 'x'.

Reorder the terms:
16x + -12x3 + 2x5 = -16x + 12x3 + 16x + -12x3

Reorder the terms:
16x + -12x3 + 2x5 = -16x + 16x + 12x3 + -12x3

Combine like terms: -16x + 16x = 0
16x + -12x3 + 2x5 = 0 + 12x3 + -12x3
16x + -12x3 + 2x5 = 12x3 + -12x3

Combine like terms: 12x3 + -12x3 = 0
16x + -12x3 + 2x5 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(8 + -6x2 + x4) = 0

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

Factor a difference between two squares.
2x((2 + -1x2)((2 + x)(2 + -1x))) = 0

Ignore the factor 2.

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 + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -1x2 = 0 Solving 2 + -1x2 = 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 + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x2 = 0 + -2 -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x2 = -2 Divide each side by '-1'. x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}

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, -1.414213562, 1.414213562, -2, 2}

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