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

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

Simplifying
5q2(q2 + 2) = 24 + -16q2

Reorder the terms:
5q2(2 + q2) = 24 + -16q2
(2 * 5q2 + q2 * 5q2) = 24 + -16q2
(10q2 + 5q4) = 24 + -16q2

Solving
10q2 + 5q4 = 24 + -16q2

Solving for variable 'q'.

Reorder the terms:
-24 + 10q2 + 16q2 + 5q4 = 24 + -16q2 + -24 + 16q2

Combine like terms: 10q2 + 16q2 = 26q2
-24 + 26q2 + 5q4 = 24 + -16q2 + -24 + 16q2

Reorder the terms:
-24 + 26q2 + 5q4 = 24 + -24 + -16q2 + 16q2

Combine like terms: 24 + -24 = 0
-24 + 26q2 + 5q4 = 0 + -16q2 + 16q2
-24 + 26q2 + 5q4 = -16q2 + 16q2

Combine like terms: -16q2 + 16q2 = 0
-24 + 26q2 + 5q4 = 0

Factor a trinomial.
(-6 + -1q2)(4 + -5q2) = 0

Subproblem 1
Set the factor '(-6 + -1q2)' equal to zero and attempt to solve:

Simplifying
-6 + -1q2 = 0

Solving
-6 + -1q2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1q2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1q2 = 0 + 6
-1q2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1q2 = 6

Divide each side by '-1'.
q2 = -6

Simplifying
q2 = -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 + -5q2)' equal to zero and attempt to solve:

Simplifying
4 + -5q2 = 0

Solving
4 + -5q2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5q2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5q2 = 0 + -4
-5q2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5q2 = -4

Divide each side by '-5'.
q2 = 0.8

Simplifying
q2 = 0.8

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