n^2+20n=-100

Solution for n^2+20n=-100 equation:

Simplifying
n2 + 20n = -100

Reorder the terms:
20n + n2 = -100

Solving
20n + n2 = -100

Solving for variable 'n'.

Reorder the terms:
100 + 20n + n2 = -100 + 100

Combine like terms: -100 + 100 = 0
100 + 20n + n2 = 0

Factor a trinomial.
(10 + n)(10 + n) = 0

Subproblem 1
Set the factor '(10 + n)' equal to zero and attempt to solve:

Simplifying
10 + n = 0

Solving
10 + n = 0

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

Add '-10' to each side of the equation.
10 + -10 + n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + n = 0 + -10
n = 0 + -10

Combine like terms: 0 + -10 = -10
n = -10

Simplifying
n = -10
Subproblem 2
Set the factor '(10 + n)' equal to zero and attempt to solve:

Simplifying
10 + n = 0

Solving
10 + n = 0

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

Add '-10' to each side of the equation.
10 + -10 + n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + n = 0 + -10
n = 0 + -10

Combine like terms: 0 + -10 = -10
n = -10

Simplifying
n = -10
Solution
n = {-10, -10}