2x^8-15x^4-27=0

Solution for 2x^8-15x^4-27=0 equation:

Simplifying
2x8 + -15x4 + -27 = 0

Reorder the terms:
-27 + -15x4 + 2x8 = 0

Solving
-27 + -15x4 + 2x8 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -2x4)(9 + -1x4) = 0

Factor a difference between two squares.
(-3 + -2x4)((3 + x2)(3 + -1x2)) = 0

Subproblem 1
Set the factor '(-3 + -2x4)' equal to zero and attempt to solve:

Simplifying
-3 + -2x4 = 0

Solving
-3 + -2x4 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x4 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x4 = 0 + 3
-2x4 = 0 + 3

Combine like terms: 0 + 3 = 3
-2x4 = 3

Divide each side by '-2'.
x4 = -1.5

Simplifying
x4 = -1.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + x2)' equal to zero and attempt to solve:

Simplifying
3 + x2 = 0

Solving
3 + x2 = 0

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

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

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

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

Simplifying
x2 = -3

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 '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-1.732050808, 1.732050808}