z^4-17z^2+72=0

Solution for z^4-17z^2+72=0 equation:

Simplifying
z4 + -17z2 + 72 = 0

Reorder the terms:
72 + -17z2 + z4 = 0

Solving
72 + -17z2 + z4 = 0

Solving for variable 'z'.

Factor a trinomial.
(8 + -1z2)(9 + -1z2) = 0

Factor a difference between two squares.
(8 + -1z2)((3 + z)(3 + -1z)) = 0

Subproblem 1
Set the factor '(8 + -1z2)' equal to zero and attempt to solve:

Simplifying
8 + -1z2 = 0

Solving
8 + -1z2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1z2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1z2 = 0 + -8
-1z2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1z2 = -8

Divide each side by '-1'.
z2 = 8

Simplifying
z2 = 8

Take the square root of each side:
z = {-2.828427125, 2.828427125}
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 = {-2.828427125, 2.828427125, -3, 3}