z^4-8z^2+12=0

Solution for z^4-8z^2+12=0 equation:

Simplifying
z4 + -8z2 + 12 = 0

Reorder the terms:
12 + -8z2 + z4 = 0

Solving
12 + -8z2 + z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + -1z2)(6 + -1z2) = 0

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

Simplifying
2 + -1z2 = 0

Solving
2 + -1z2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z2 = 0 + -2

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

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

Divide each side by '-1'.
z2 = 2

Simplifying
z2 = 2

Take the square root of each side:
z = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(6 + -1z2)' equal to zero and attempt to solve:

Simplifying
6 + -1z2 = 0

Solving
6 + -1z2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z2 = 0 + -6
-1z2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1z2 = -6

Divide each side by '-1'.
z2 = 6

Simplifying
z2 = 6

Take the square root of each side:
z = {-2.449489743, 2.449489743}
Solution
z = {-1.414213562, 1.414213562, -2.449489743, 2.449489743}