12x^4-27=0

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

Simplifying
12x4 + -27 = 0

Reorder the terms:
-27 + 12x4 = 0

Solving
-27 + 12x4 = 0

Solving for variable 'x'.

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

Add '27' to each side of the equation.
-27 + 27 + 12x4 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 12x4 = 0 + 27
12x4 = 0 + 27

Combine like terms: 0 + 27 = 27
12x4 = 27

Divide each side by '12'.
x4 = 2.25

Simplifying
x4 = 2.25

Reorder the terms:
-2.25 + x4 = 2.25 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
-2.25 + x4 = 0.00

Factor a difference between two squares.
(1.5 + x2)(-1.5 + x2) = 0.00

Subproblem 1
Set the factor '(1.5 + x2)' equal to zero and attempt to solve:

Simplifying
1.5 + x2 = 0

Solving
1.5 + x2 = 0

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x2 = 0 + -1.5
x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
x2 = -1.5

Simplifying
x2 = -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 '(-1.5 + x2)' equal to zero and attempt to solve:

Simplifying
-1.5 + x2 = 0

Solving
-1.5 + x2 = 0

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x2 = 0 + 1.5
x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
x2 = 1.5

Simplifying
x2 = 1.5

Take the square root of each side:
x = {-1.224744871, 1.224744871}
Solution
x = {-1.224744871, 1.224744871}