4n^2+16=-20n

Solution for 4n^2+16=-20n equation:

Simplifying
4n2 + 16 = -20n

Reorder the terms:
16 + 4n2 = -20n

Solving
16 + 4n2 = -20n

Solving for variable 'n'.

Reorder the terms:
16 + 20n + 4n2 = -20n + 20n

Combine like terms: -20n + 20n = 0
16 + 20n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + 5n + n2) = 0

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

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

Simplifying
4 + n = 0

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

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

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

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

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

Simplifying
n = -1
Solution
n = {-4, -1}