81x^6-(x^2)=0

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


Simplifying
81x6 + -1(x2) = 0

Reorder the terms:
-1x2 + 81x6 = 0

Solving
-1x2 + 81x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-1 + 81x4) = 0

Factor a difference between two squares.
x2((1 + 9x2)(-1 + 9x2)) = 0

Factor a difference between two squares.
x2((1 + 9x2)((1 + 3x)(-1 + 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 '(1 + 9x2)' equal to zero and attempt to solve:

Simplifying
1 + 9x2 = 0

Solving
1 + 9x2 = 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 + 9x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9x2 = 0 + -1
9x2 = 0 + -1

Combine like terms: 0 + -1 = -1
9x2 = -1

Divide each side by '9'.
x2 = -0.1111111111

Simplifying
x2 = -0.1111111111

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 '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 4
Set the factor '(-1 + 3x)' equal to zero and attempt to solve:

Simplifying
-1 + 3x = 0

Solving
-1 + 3x = 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 + 3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3x = 0 + 1
3x = 0 + 1

Combine like terms: 0 + 1 = 1
3x = 1

Divide each side by '3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, -0.3333333333, 0.3333333333}

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