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

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

Simplifying
2x4 + -15x2 + 27 = 0

Reorder the terms:
27 + -15x2 + 2x4 = 0

Solving
27 + -15x2 + 2x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x2)(9 + -2x2) = 0

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

Simplifying
9 + -2x2 = 0

Solving
9 + -2x2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x2 = 0 + -9

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

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

Divide each side by '-2'.
x2 = 4.5

Simplifying
x2 = 4.5

Take the square root of each side:
x = {-2.121320344, 2.121320344}
Solution
x = {-1.732050808, 1.732050808, -2.121320344, 2.121320344}