4x^4-16x^2-9=0

Solution for 4x^4-16x^2-9=0 equation:

Simplifying
4x4 + -16x2 + -9 = 0

Reorder the terms:
-9 + -16x2 + 4x4 = 0

Solving
-9 + -16x2 + 4x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -2x2)(9 + -2x2) = 0

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

Simplifying
-1 + -2x2 = 0

Solving
-1 + -2x2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x2 = 0 + 1

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

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

Divide each side by '-2'.
x2 = -0.5

Simplifying
x2 = -0.5

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 '(9 + -2x2)' equal to zero and attempt to solve:

Simplifying
9 + -2x2 = 0

Solving
9 + -2x2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x2 = 0 + -9
-2x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-2x2 = -9

Divide each side by '-2'.
x2 = 4.5

Simplifying
x2 = 4.5

Take the square root of each side:
x = {-2.121320344, 2.121320344}
Solution
x = {-2.121320344, 2.121320344}