3n^2(n^2+4)=24-2n^2

Solution for 3n^2(n^2+4)=24-2n^2 equation:

Simplifying
3n2(n2 + 4) = 24 + -2n2

Reorder the terms:
3n2(4 + n2) = 24 + -2n2
(4 * 3n2 + n2 * 3n2) = 24 + -2n2
(12n2 + 3n4) = 24 + -2n2

Solving
12n2 + 3n4 = 24 + -2n2

Solving for variable 'n'.

Reorder the terms:
-24 + 12n2 + 2n2 + 3n4 = 24 + -2n2 + -24 + 2n2

Combine like terms: 12n2 + 2n2 = 14n2
-24 + 14n2 + 3n4 = 24 + -2n2 + -24 + 2n2

Reorder the terms:
-24 + 14n2 + 3n4 = 24 + -24 + -2n2 + 2n2

Combine like terms: 24 + -24 = 0
-24 + 14n2 + 3n4 = 0 + -2n2 + 2n2
-24 + 14n2 + 3n4 = -2n2 + 2n2

Combine like terms: -2n2 + 2n2 = 0
-24 + 14n2 + 3n4 = 0

Factor a trinomial.
(-6 + -1n2)(4 + -3n2) = 0

Subproblem 1
Set the factor '(-6 + -1n2)' equal to zero and attempt to solve:

Simplifying
-6 + -1n2 = 0

Solving
-6 + -1n2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n2 = 0 + 6
-1n2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1n2 = 6

Divide each side by '-1'.
n2 = -6

Simplifying
n2 = -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 + -3n2)' equal to zero and attempt to solve:

Simplifying
4 + -3n2 = 0

Solving
4 + -3n2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3n2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3n2 = 0 + -4
-3n2 = 0 + -4

Combine like terms: 0 + -4 = -4
-3n2 = -4

Divide each side by '-3'.
n2 = 1.333333333

Simplifying
n2 = 1.333333333

Take the square root of each side:
n = {-1.154700538, 1.154700538}
Solution
n = {-1.154700538, 1.154700538}