3x^4-8x^2-16=0

Solution for 3x^4-8x^2-16=0 equation:

Simplifying
3x4 + -8x2 + -16 = 0

Reorder the terms:
-16 + -8x2 + 3x4 = 0

Solving
-16 + -8x2 + 3x4 = 0

Solving for variable 'x'.

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

Factor a difference between two squares.
(-4 + -3x2)((2 + x)(2 + -1x)) = 0

Subproblem 1
Set the factor '(-4 + -3x2)' equal to zero and attempt to solve:

Simplifying
-4 + -3x2 = 0

Solving
-4 + -3x2 = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x2 = 0 + 4
-3x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-3x2 = 4

Divide each side by '-3'.
x2 = -1.333333333

Simplifying
x2 = -1.333333333

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}