5x^5-18x^3+16x=0

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Solution for 5x^5-18x^3+16x=0 equation: 


Simplifying
5x5 + -18x3 + 16x = 0

Reorder the terms:
16x + -18x3 + 5x5 = 0

Solving
16x + -18x3 + 5x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(16 + -18x2 + 5x4) = 0

Factor a trinomial.
x((8 + -5x2)(2 + -1x2)) = 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 '(8 + -5x2)' equal to zero and attempt to solve:

Simplifying
8 + -5x2 = 0

Solving
8 + -5x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -5x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x2 = 0 + -8
-5x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-5x2 = -8

Divide each side by '-5'.
x2 = 1.6

Simplifying
x2 = 1.6

Take the square root of each side:
x = {-1.264911064, 1.264911064}

Subproblem 3
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}
Solution
x = {0, -1.264911064, 1.264911064, -1.414213562, 1.414213562}

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