5n^2(n^2+2)=112-9n^2

Solution for 5n^2(n^2+2)=112-9n^2 equation:

Simplifying
5n2(n2 + 2) = 112 + -9n2

Reorder the terms:
5n2(2 + n2) = 112 + -9n2
(2 * 5n2 + n2 * 5n2) = 112 + -9n2
(10n2 + 5n4) = 112 + -9n2

Solving
10n2 + 5n4 = 112 + -9n2

Solving for variable 'n'.

Reorder the terms:
-112 + 10n2 + 9n2 + 5n4 = 112 + -9n2 + -112 + 9n2

Combine like terms: 10n2 + 9n2 = 19n2
-112 + 19n2 + 5n4 = 112 + -9n2 + -112 + 9n2

Reorder the terms:
-112 + 19n2 + 5n4 = 112 + -112 + -9n2 + 9n2

Combine like terms: 112 + -112 = 0
-112 + 19n2 + 5n4 = 0 + -9n2 + 9n2
-112 + 19n2 + 5n4 = -9n2 + 9n2

Combine like terms: -9n2 + 9n2 = 0
-112 + 19n2 + 5n4 = 0

Factor a trinomial.
(-7 + -1n2)(16 + -5n2) = 0

Subproblem 1
Set the factor '(-7 + -1n2)' equal to zero and attempt to solve:

Simplifying
-7 + -1n2 = 0

Solving
-7 + -1n2 = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n2 = 0 + 7
-1n2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1n2 = 7

Divide each side by '-1'.
n2 = -7

Simplifying
n2 = -7

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 + -5n2)' equal to zero and attempt to solve:

Simplifying
16 + -5n2 = 0

Solving
16 + -5n2 = 0

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

Add '-16' to each side of the equation.
16 + -16 + -5n2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -5n2 = 0 + -16
-5n2 = 0 + -16

Combine like terms: 0 + -16 = -16
-5n2 = -16

Divide each side by '-5'.
n2 = 3.2

Simplifying
n2 = 3.2

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