16x^5-76x^3=-90x

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Solution for 16x^5-76x^3=-90x equation:


Simplifying
16x5 + -76x3 = -90x

Reorder the terms:
-76x3 + 16x5 = -90x

Solving
-76x3 + 16x5 = -90x

Solving for variable 'x'.

Reorder the terms:
90x + -76x3 + 16x5 = -90x + 90x

Combine like terms: -90x + 90x = 0
90x + -76x3 + 16x5 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(45 + -38x2 + 8x4) = 0

Factor a trinomial.
2x((9 + -4x2)(5 + -2x2)) = 0

Factor a difference between two squares.
2x(((3 + 2x)(3 + -2x))(5 + -2x2)) = 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 '(5 + -2x2)' equal to zero and attempt to solve: Simplifying 5 + -2x2 = 0 Solving 5 + -2x2 = 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 + -2x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x2 = 0 + -5 -2x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -2x2 = -5 Divide each side by '-2'. x2 = 2.5 Simplifying x2 = 2.5 Take the square root of each side: x = {-1.58113883, 1.58113883}

Subproblem 3

Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

Subproblem 4

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Solution

x = {0, -1.58113883, 1.58113883, -1.5, 1.5}

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