y^2+20y+19=0

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

Simplifying
y2 + 20y + 19 = 0

Reorder the terms:
19 + 20y + y2 = 0

Solving
19 + 20y + y2 = 0

Solving for variable 'y'.

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

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

Simplifying
19 + y = 0

Solving
19 + y = 0

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

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

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

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

Simplifying
y = -19
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

Simplifying
y = -1
Solution
y = {-19, -1}