15x^4-12x^2-27=0

Solution for 15x^4-12x^2-27=0 equation:

Simplifying
15x4 + -12x2 + -27 = 0

Reorder the terms:
-27 + -12x2 + 15x4 = 0

Solving
-27 + -12x2 + 15x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -4x2 + 5x4) = 0

Factor a trinomial.
3((-1 + -1x2)(9 + -5x2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -1x2)' equal to zero and attempt to solve:

Simplifying
-1 + -1x2 = 0

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

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

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

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

Simplifying
x2 = -1

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 '(9 + -5x2)' equal to zero and attempt to solve:

Simplifying
9 + -5x2 = 0

Solving
9 + -5x2 = 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 + -5x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x2 = 0 + -9
-5x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-5x2 = -9

Divide each side by '-5'.
x2 = 1.8

Simplifying
x2 = 1.8

Take the square root of each side:
x = {-1.341640787, 1.341640787}
Solution
x = {-1.341640787, 1.341640787}