3x^5-2x^3=5x

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


Simplifying
3x5 + -2x3 = 5x

Reorder the terms:
-2x3 + 3x5 = 5x

Solving
-2x3 + 3x5 = 5x

Solving for variable 'x'.

Reorder the terms:
-5x + -2x3 + 3x5 = 5x + -5x

Combine like terms: 5x + -5x = 0
-5x + -2x3 + 3x5 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + -2x2 + 3x4) = 0

Factor a trinomial.
x((-1 + -1x2)(5 + -3x2)) = 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 '(-1 + -1x2)' equal to zero and attempt to solve: Simplifying -1 + -1x2 = 0 Solving -1 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x2 = 0 + 1 -1x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1x2 = 1 Divide each side by '-1'. x2 = -1 Simplifying x2 = -1 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 '(5 + -3x2)' equal to zero and attempt to solve: Simplifying 5 + -3x2 = 0 Solving 5 + -3x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x2 = 0 + -5 -3x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3x2 = -5 Divide each side by '-3'. x2 = 1.666666667 Simplifying x2 = 1.666666667 Take the square root of each side: x = {-1.290994449, 1.290994449}

Solution

x = {0, -1.290994449, 1.290994449}

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