6z^4+z^2-1=0

Solution for 6z^4+z^2-1=0 equation:

Simplifying
6z4 + z2 + -1 = 0

Reorder the terms:
-1 + z2 + 6z4 = 0

Solving
-1 + z2 + 6z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -2z2)(1 + -3z2) = 0

Subproblem 1
Set the factor '(-1 + -2z2)' equal to zero and attempt to solve:

Simplifying
-1 + -2z2 = 0

Solving
-1 + -2z2 = 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 + -2z2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2z2 = 0 + 1
-2z2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2z2 = 1

Divide each side by '-2'.
z2 = -0.5

Simplifying
z2 = -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 '(1 + -3z2)' equal to zero and attempt to solve:

Simplifying
1 + -3z2 = 0

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

Combine like terms: 1 + -1 = 0
0 + -3z2 = 0 + -1
-3z2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3z2 = -1

Divide each side by '-3'.
z2 = 0.3333333333

Simplifying
z2 = 0.3333333333

Take the square root of each side:
z = {-0.577350269, 0.577350269}
Solution
z = {-0.577350269, 0.577350269}