y(y+3)+2(y+3)=0

Solution for y(y+3)+2(y+3)=0 equation:

Simplifying
y(y + 3) + 2(y + 3) = 0

Reorder the terms:
y(3 + y) + 2(y + 3) = 0
(3 * y + y * y) + 2(y + 3) = 0
(3y + y2) + 2(y + 3) = 0

Reorder the terms:
3y + y2 + 2(3 + y) = 0
3y + y2 + (3 * 2 + y * 2) = 0
3y + y2 + (6 + 2y) = 0

Reorder the terms:
6 + 3y + 2y + y2 = 0

Combine like terms: 3y + 2y = 5y
6 + 5y + y2 = 0

Solving
6 + 5y + y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

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

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

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

Simplifying
2 + y = 0

Solving
2 + y = 0

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

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

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

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

Simplifying
y = -2
Solution
y = {-3, -2}