0=18x^5-32x

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Solution for 0=18x^5-32x equation: 


Simplifying
0 = 18x5 + -32x

Reorder the terms:
0 = -32x + 18x5

Solving
0 = -32x + 18x5

Solving for variable 'x'.
Remove the zero:
32x + -18x5 = -32x + 18x5 + 32x + -18x5

Reorder the terms:
32x + -18x5 = -32x + 32x + 18x5 + -18x5

Combine like terms: -32x + 32x = 0
32x + -18x5 = 0 + 18x5 + -18x5
32x + -18x5 = 18x5 + -18x5

Combine like terms: 18x5 + -18x5 = 0
32x + -18x5 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(16 + -9x4) = 0

Factor a difference between two squares.
2x((4 + 3x2)(4 + -3x2)) = 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 '(4 + 3x2)' equal to zero and attempt to solve:

Simplifying
4 + 3x2 = 0

Solving
4 + 3x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x2 = 0 + -4
3x2 = 0 + -4

Combine like terms: 0 + -4 = -4
3x2 = -4

Divide each side by '3'.
x2 = -1.333333333

Simplifying
x2 = -1.333333333

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 '(4 + -3x2)' equal to zero and attempt to solve:

Simplifying
4 + -3x2 = 0

Solving
4 + -3x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x2 = 0 + -4
-3x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-3x2 = -4

Divide each side by '-3'.
x2 = 1.333333333

Simplifying
x2 = 1.333333333

Take the square root of each side:
x = {-1.154700538, 1.154700538}
Solution
x = {0, -1.154700538, 1.154700538}

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