-2x^4+x^2+6=0

Solution for -2x^4+x^2+6=0 equation:

Simplifying
-2x4 + x2 + 6 = 0

Reorder the terms:
6 + x2 + -2x4 = 0

Solving
6 + x2 + -2x4 = 0

Solving for variable 'x'.

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

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

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 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 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Subproblem 2
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.
Solution
x = {-1.414213562, 1.414213562}