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

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

Simplifying
2z4 + -3z2 + 1 = 0

Reorder the terms:
1 + -3z2 + 2z4 = 0

Solving
1 + -3z2 + 2z4 = 0

Solving for variable 'z'.

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

Factor a difference between two squares.
(1 + -2z2)((1 + z)(1 + -1z)) = 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

Take the square root of each side:
z = {-0.707106781, 0.707106781}
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 = {-0.707106781, 0.707106781, -1, 1}