0=3x^4-x^2-24

Solution for 0=3x^4-x^2-24 equation:

Simplifying
0 = 3x4 + -1x2 + -24

Reorder the terms:
0 = -24 + -1x2 + 3x4

Solving
0 = -24 + -1x2 + 3x4

Solving for variable 'x'.

Combine like terms: 0 + 24 = 24
24 + x2 + -3x4 = -24 + -1x2 + 3x4 + 24 + x2 + -3x4

Reorder the terms:
24 + x2 + -3x4 = -24 + 24 + -1x2 + x2 + 3x4 + -3x4

Combine like terms: -24 + 24 = 0
24 + x2 + -3x4 = 0 + -1x2 + x2 + 3x4 + -3x4
24 + x2 + -3x4 = -1x2 + x2 + 3x4 + -3x4

Combine like terms: -1x2 + x2 = 0
24 + x2 + -3x4 = 0 + 3x4 + -3x4
24 + x2 + -3x4 = 3x4 + -3x4

Combine like terms: 3x4 + -3x4 = 0
24 + x2 + -3x4 = 0

Factor a trinomial.
(3 + -1x2)(8 + 3x2) = 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 '(8 + 3x2)' equal to zero and attempt to solve:

Simplifying
8 + 3x2 = 0

Solving
8 + 3x2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x2 = 0 + -8
3x2 = 0 + -8

Combine like terms: 0 + -8 = -8
3x2 = -8

Divide each side by '3'.
x2 = -2.666666667

Simplifying
x2 = -2.666666667

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-1.732050808, 1.732050808}