81x^4-27x^2+2=0

Solution for 81x^4-27x^2+2=0 equation:

Simplifying
81x4 + -27x2 + 2 = 0

Reorder the terms:
2 + -27x2 + 81x4 = 0

Solving
2 + -27x2 + 81x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -9x2)(2 + -9x2) = 0

Factor a difference between two squares.
((1 + 3x)(1 + -3x))(2 + -9x2) = 0

Subproblem 1
Set the factor '(2 + -9x2)' equal to zero and attempt to solve:

Simplifying
2 + -9x2 = 0

Solving
2 + -9x2 = 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 + -9x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9x2 = 0 + -2
-9x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-9x2 = -2

Divide each side by '-9'.
x2 = 0.2222222222

Simplifying
x2 = 0.2222222222

Take the square root of each side:
x = {-0.471404521, 0.471404521}
Subproblem 2
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 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
Solution
x = {-0.471404521, 0.471404521, -0.3333333333, 0.3333333333}