y^2+19y=-78

Solution for y^2+19y=-78 equation:

Simplifying
y2 + 19y = -78

Reorder the terms:
19y + y2 = -78

Solving
19y + y2 = -78

Solving for variable 'y'.

Reorder the terms:
78 + 19y + y2 = -78 + 78

Combine like terms: -78 + 78 = 0
78 + 19y + y2 = 0

Factor a trinomial.
(13 + y)(6 + y) = 0

Subproblem 1
Set the factor '(13 + y)' equal to zero and attempt to solve:

Simplifying
13 + y = 0

Solving
13 + y = 0

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

Add '-13' to each side of the equation.
13 + -13 + y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + y = 0 + -13
y = 0 + -13

Combine like terms: 0 + -13 = -13
y = -13

Simplifying
y = -13
Subproblem 2
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Solution
y = {-13, -6}