5z^2(z^2+2)=24-16z^2

Solution for 5z^2(z^2+2)=24-16z^2 equation:

Simplifying
5z2(z2 + 2) = 24 + -16z2

Reorder the terms:
5z2(2 + z2) = 24 + -16z2
(2 * 5z2 + z2 * 5z2) = 24 + -16z2
(10z2 + 5z4) = 24 + -16z2

Solving
10z2 + 5z4 = 24 + -16z2

Solving for variable 'z'.

Reorder the terms:
-24 + 10z2 + 16z2 + 5z4 = 24 + -16z2 + -24 + 16z2

Combine like terms: 10z2 + 16z2 = 26z2
-24 + 26z2 + 5z4 = 24 + -16z2 + -24 + 16z2

Reorder the terms:
-24 + 26z2 + 5z4 = 24 + -24 + -16z2 + 16z2

Combine like terms: 24 + -24 = 0
-24 + 26z2 + 5z4 = 0 + -16z2 + 16z2
-24 + 26z2 + 5z4 = -16z2 + 16z2

Combine like terms: -16z2 + 16z2 = 0
-24 + 26z2 + 5z4 = 0

Factor a trinomial.
(-6 + -1z2)(4 + -5z2) = 0

Subproblem 1
Set the factor '(-6 + -1z2)' equal to zero and attempt to solve:

Simplifying
-6 + -1z2 = 0

Solving
-6 + -1z2 = 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 + -1z2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z2 = 0 + 6
-1z2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1z2 = 6

Divide each side by '-1'.
z2 = -6

Simplifying
z2 = -6

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 '(4 + -5z2)' equal to zero and attempt to solve:

Simplifying
4 + -5z2 = 0

Solving
4 + -5z2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5z2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5z2 = 0 + -4
-5z2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5z2 = -4

Divide each side by '-5'.
z2 = 0.8

Simplifying
z2 = 0.8

Take the square root of each side:
z = {-0.894427191, 0.894427191}
Solution
z = {-0.894427191, 0.894427191}