2n^2+50=-20n

Solution for 2n^2+50=-20n equation:

Simplifying
2n2 + 50 = -20n

Reorder the terms:
50 + 2n2 = -20n

Solving
50 + 2n2 = -20n

Solving for variable 'n'.

Reorder the terms:
50 + 20n + 2n2 = -20n + 20n

Combine like terms: -20n + 20n = 0
50 + 20n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 10n + n2) = 0

Factor a trinomial.
2((5 + n)(5 + n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

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

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

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

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Solution
n = {-5, -5}