-4n^2-16=-8+2n-5n^2

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Solution for -4n^2-16=-8+2n-5n^2 equation: 


Simplifying
-4n2 + -16 = -8 + 2n + -5n2

Reorder the terms:
-16 + -4n2 = -8 + 2n + -5n2

Solving
-16 + -4n2 = -8 + 2n + -5n2

Solving for variable 'n'.

Reorder the terms:
-16 + 8 + -2n + -4n2 + 5n2 = -8 + 2n + -5n2 + 8 + -2n + 5n2

Combine like terms: -16 + 8 = -8
-8 + -2n + -4n2 + 5n2 = -8 + 2n + -5n2 + 8 + -2n + 5n2

Combine like terms: -4n2 + 5n2 = 1n2
-8 + -2n + 1n2 = -8 + 2n + -5n2 + 8 + -2n + 5n2

Reorder the terms:
-8 + -2n + 1n2 = -8 + 8 + 2n + -2n + -5n2 + 5n2

Combine like terms: -8 + 8 = 0
-8 + -2n + 1n2 = 0 + 2n + -2n + -5n2 + 5n2
-8 + -2n + 1n2 = 2n + -2n + -5n2 + 5n2

Combine like terms: 2n + -2n = 0
-8 + -2n + 1n2 = 0 + -5n2 + 5n2
-8 + -2n + 1n2 = -5n2 + 5n2

Combine like terms: -5n2 + 5n2 = 0
-8 + -2n + 1n2 = 0

Factor a trinomial.
(-2 + -1n)(4 + -1n) = 0


Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

Simplifying
n = -2

Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 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 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-2, 4}

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