n^2+20n+19=0

Solution for n^2+20n+19=0 equation:

Simplifying
n2 + 20n + 19 = 0

Reorder the terms:
19 + 20n + n2 = 0

Solving
19 + 20n + n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(19 + n)' equal to zero and attempt to solve:

Simplifying
19 + n = 0

Solving
19 + n = 0

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

Add '-19' to each side of the equation.
19 + -19 + n = 0 + -19

Combine like terms: 19 + -19 = 0
0 + n = 0 + -19
n = 0 + -19

Combine like terms: 0 + -19 = -19
n = -19

Simplifying
n = -19
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 = {-19, -1}