(z^4-4)(z^4-9)=

Solution for (z^4-4)(z^4-9)= equation:

Simplifying
(z4 + -4)(z4 + -9) = 0

Reorder the terms:
(-4 + z4)(z4 + -9) = 0

Reorder the terms:
(-4 + z4)(-9 + z4) = 0

Multiply (-4 + z4) * (-9 + z4)
(-4(-9 + z4) + z4(-9 + z4)) = 0
((-9 * -4 + z4 * -4) + z4(-9 + z4)) = 0
((36 + -4z4) + z4(-9 + z4)) = 0
(36 + -4z4 + (-9 * z4 + z4 * z4)) = 0
(36 + -4z4 + (-9z4 + z8)) = 0

Combine like terms: -4z4 + -9z4 = -13z4
(36 + -13z4 + z8) = 0

Solving
36 + -13z4 + z8 = 0

Solving for variable 'z'.

Factor a trinomial.
(4 + -1z4)(9 + -1z4) = 0

Factor a difference between two squares.
((2 + z2)(2 + -1z2))(9 + -1z4) = 0

Factor a difference between two squares.
((3 + z2)(3 + -1z2))(2 + z2)(2 + -1z2) = 0

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

Simplifying
2 + z2 = 0

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

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

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

Simplifying
z2 = -2

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

Simplifying
3 + z2 = 0

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

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

Combine like terms: 0 + -3 = -3
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 4
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

Take the square root of each side:
z = {-1.732050808, 1.732050808}
Solution
z = {-1.414213562, 1.414213562, -1.732050808, 1.732050808}