0=2x^4-5x^2-12

Solution for 0=2x^4-5x^2-12 equation:

Simplifying
0 = 2x4 + -5x2 + -12

Reorder the terms:
0 = -12 + -5x2 + 2x4

Solving
0 = -12 + -5x2 + 2x4

Solving for variable 'x'.

Combine like terms: 0 + 12 = 12
12 + 5x2 + -2x4 = -12 + -5x2 + 2x4 + 12 + 5x2 + -2x4

Reorder the terms:
12 + 5x2 + -2x4 = -12 + 12 + -5x2 + 5x2 + 2x4 + -2x4

Combine like terms: -12 + 12 = 0
12 + 5x2 + -2x4 = 0 + -5x2 + 5x2 + 2x4 + -2x4
12 + 5x2 + -2x4 = -5x2 + 5x2 + 2x4 + -2x4

Combine like terms: -5x2 + 5x2 = 0
12 + 5x2 + -2x4 = 0 + 2x4 + -2x4
12 + 5x2 + -2x4 = 2x4 + -2x4

Combine like terms: 2x4 + -2x4 = 0
12 + 5x2 + -2x4 = 0

Factor a trinomial.
(4 + -1x2)(3 + 2x2) = 0

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

Subproblem 1
Set the factor '(3 + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + 2x2 = 0

Solving
3 + 2x2 = 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 + 2x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x2 = 0 + -3
2x2 = 0 + -3

Combine like terms: 0 + -3 = -3
2x2 = -3

Divide each side by '2'.
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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2, 2}