z^4-6z^2=27

Solution for z^4-6z^2=27 equation:

Simplifying
z4 + -6z2 = 27

Reorder the terms:
-6z2 + z4 = 27

Solving
-6z2 + z4 = 27

Solving for variable 'z'.

Reorder the terms:
-27 + -6z2 + z4 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + -6z2 + z4 = 0

Factor a trinomial.
(-3 + -1z2)(9 + -1z2) = 0

Factor a difference between two squares.
(-3 + -1z2)((3 + z)(3 + -1z)) = 0

Subproblem 1
Set the factor '(-3 + -1z2)' equal to zero and attempt to solve:

Simplifying
-3 + -1z2 = 0

Solving
-3 + -1z2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1z2 = 0 + 3

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

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

Divide each side by '-1'.
z2 = -3

Simplifying
z2 = -3

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

Simplifying
3 + z = 0

Solving
3 + z = 0

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

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

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

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

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

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

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {-3, 3}