5z^2(z^2-2)=32-4z^2

Solution for 5z^2(z^2-2)=32-4z^2 equation:

Simplifying
5z2(z2 + -2) = 32 + -4z2

Reorder the terms:
5z2(-2 + z2) = 32 + -4z2
(-2 * 5z2 + z2 * 5z2) = 32 + -4z2
(-10z2 + 5z4) = 32 + -4z2

Solving
-10z2 + 5z4 = 32 + -4z2

Solving for variable 'z'.

Reorder the terms:
-32 + -10z2 + 4z2 + 5z4 = 32 + -4z2 + -32 + 4z2

Combine like terms: -10z2 + 4z2 = -6z2
-32 + -6z2 + 5z4 = 32 + -4z2 + -32 + 4z2

Reorder the terms:
-32 + -6z2 + 5z4 = 32 + -32 + -4z2 + 4z2

Combine like terms: 32 + -32 = 0
-32 + -6z2 + 5z4 = 0 + -4z2 + 4z2
-32 + -6z2 + 5z4 = -4z2 + 4z2

Combine like terms: -4z2 + 4z2 = 0
-32 + -6z2 + 5z4 = 0

Factor a trinomial.
(-2 + -1z2)(16 + -5z2) = 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

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 '(16 + -5z2)' equal to zero and attempt to solve:

Simplifying
16 + -5z2 = 0

Solving
16 + -5z2 = 0

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

Add '-16' to each side of the equation.
16 + -16 + -5z2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -5z2 = 0 + -16
-5z2 = 0 + -16

Combine like terms: 0 + -16 = -16
-5z2 = -16

Divide each side by '-5'.
z2 = 3.2

Simplifying
z2 = 3.2

Take the square root of each side:
z = {-1.788854382, 1.788854382}
Solution
z = {-1.788854382, 1.788854382}