x^5=x^3+12x

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Solution for x^5=x^3+12x equation:


Simplifying
x5 = x3 + 12x

Reorder the terms:
x5 = 12x + x3

Solving
x5 = 12x + x3

Solving for variable 'x'.

Reorder the terms:
-12x + -1x3 + x5 = 12x + x3 + -12x + -1x3

Reorder the terms:
-12x + -1x3 + x5 = 12x + -12x + x3 + -1x3

Combine like terms: 12x + -12x = 0
-12x + -1x3 + x5 = 0 + x3 + -1x3
-12x + -1x3 + x5 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-12x + -1x3 + x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-12 + -1x2 + x4) = 0

Factor a trinomial.
x((-3 + -1x2)(4 + -1x2)) = 0

Factor a difference between two squares.
x((-3 + -1x2)((2 + x)(2 + -1x))) = 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 '(-3 + -1x2)' equal to zero and attempt to solve: Simplifying -3 + -1x2 = 0 Solving -3 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x2 = 0 + 3 -1x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1x2 = 3 Divide each side by '-1'. x2 = -3 Simplifying x2 = -3 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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