2y^2+19y=-24

Solution for 2y^2+19y=-24 equation:

Simplifying
2y2 + 19y = -24

Reorder the terms:
19y + 2y2 = -24

Solving
19y + 2y2 = -24

Solving for variable 'y'.

Reorder the terms:
24 + 19y + 2y2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + 19y + 2y2 = 0

Factor a trinomial.
(8 + y)(3 + 2y) = 0

Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Simplifying
y = -8
Subproblem 2
Set the factor '(3 + 2y)' equal to zero and attempt to solve:

Simplifying
3 + 2y = 0

Solving
3 + 2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Solution
y = {-8, -1.5}