81x^6-16x^2=0

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Solution for 81x^6-16x^2=0 equation: 


Simplifying
81x6 + -16x2 = 0

Reorder the terms:
-16x2 + 81x6 = 0

Solving
-16x2 + 81x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-16 + 81x4) = 0

Factor a difference between two squares.
x2((4 + 9x2)(-4 + 9x2)) = 0

Factor a difference between two squares.
x2((4 + 9x2)((2 + 3x)(-2 + 3x))) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(4 + 9x2)' equal to zero and attempt to solve:

Simplifying
4 + 9x2 = 0

Solving
4 + 9x2 = 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 + 9x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 9x2 = 0 + -4
9x2 = 0 + -4

Combine like terms: 0 + -4 = -4
9x2 = -4

Divide each side by '9'.
x2 = -0.4444444444

Simplifying
x2 = -0.4444444444

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 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 4
Set the factor '(-2 + 3x)' equal to zero and attempt to solve:

Simplifying
-2 + 3x = 0

Solving
-2 + 3x = 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 + 3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x = 0 + 2
3x = 0 + 2

Combine like terms: 0 + 2 = 2
3x = 2

Divide each side by '3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {0, -0.6666666667, 0.6666666667}

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