(Z^2-36)(Z^2-18)=0

Solution for (Z^2-36)(Z^2-18)=0 equation:

Simplifying
(Z2 + -36)(Z2 + -18) = 0

Reorder the terms:
(-36 + Z2)(Z2 + -18) = 0

Reorder the terms:
(-36 + Z2)(-18 + Z2) = 0

Multiply (-36 + Z2) * (-18 + Z2)
(-36(-18 + Z2) + Z2(-18 + Z2)) = 0
((-18 * -36 + Z2 * -36) + Z2(-18 + Z2)) = 0
((648 + -36Z2) + Z2(-18 + Z2)) = 0
(648 + -36Z2 + (-18 * Z2 + Z2 * Z2)) = 0
(648 + -36Z2 + (-18Z2 + Z4)) = 0

Combine like terms: -36Z2 + -18Z2 = -54Z2
(648 + -54Z2 + Z4) = 0

Solving
648 + -54Z2 + Z4 = 0

Solving for variable 'Z'.

Factor a trinomial.
(18 + -1Z2)(36 + -1Z2) = 0

Factor a difference between two squares.
(18 + -1Z2)((6 + Z)(6 + -1Z)) = 0

Subproblem 1
Set the factor '(18 + -1Z2)' equal to zero and attempt to solve:

Simplifying
18 + -1Z2 = 0

Solving
18 + -1Z2 = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1Z2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1Z2 = 0 + -18
-1Z2 = 0 + -18

Combine like terms: 0 + -18 = -18
-1Z2 = -18

Divide each side by '-1'.
Z2 = 18

Simplifying
Z2 = 18

Take the square root of each side:
Z = {-4.242640687, 4.242640687}
Subproblem 2
Set the factor '(6 + Z)' equal to zero and attempt to solve:

Simplifying
6 + Z = 0

Solving
6 + Z = 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 + Z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + Z = 0 + -6
Z = 0 + -6

Combine like terms: 0 + -6 = -6
Z = -6

Simplifying
Z = -6
Subproblem 3
Set the factor '(6 + -1Z)' equal to zero and attempt to solve:

Simplifying
6 + -1Z = 0

Solving
6 + -1Z = 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 + -1Z = 0 + -6

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

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

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

Simplifying
Z = 6
Solution
Z = {-4.242640687, 4.242640687, -6, 6}