4z^4-3z^2-1=0

Solution for 4z^4-3z^2-1=0 equation:

Simplifying
4z4 + -3z2 + -1 = 0

Reorder the terms:
-1 + -3z2 + 4z4 = 0

Solving
-1 + -3z2 + 4z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -4z2)(1 + -1z2) = 0

Factor a difference between two squares.
(-1 + -4z2)((1 + z)(1 + -1z)) = 0

Subproblem 1
Set the factor '(-1 + -4z2)' equal to zero and attempt to solve:

Simplifying
-1 + -4z2 = 0

Solving
-1 + -4z2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4z2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4z2 = 0 + 1
-4z2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4z2 = 1

Divide each side by '-4'.
z2 = -0.25

Simplifying
z2 = -0.25

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 '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

Combine like terms: 1 + -1 = 0
0 + z = 0 + -1
z = 0 + -1

Combine like terms: 0 + -1 = -1
z = -1

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1z = 0 + -1
-1z = 0 + -1

Combine like terms: 0 + -1 = -1
-1z = -1

Divide each side by '-1'.
z = 1

Simplifying
z = 1
Solution
z = {-1, 1}