y(2y+1)+3(2y+1)=0

Solution for y(2y+1)+3(2y+1)=0 equation:

Simplifying
y(2y + 1) + 3(2y + 1) = 0

Reorder the terms:
y(1 + 2y) + 3(2y + 1) = 0
(1 * y + 2y * y) + 3(2y + 1) = 0
(1y + 2y2) + 3(2y + 1) = 0

Reorder the terms:
1y + 2y2 + 3(1 + 2y) = 0
1y + 2y2 + (1 * 3 + 2y * 3) = 0
1y + 2y2 + (3 + 6y) = 0

Reorder the terms:
3 + 1y + 6y + 2y2 = 0

Combine like terms: 1y + 6y = 7y
3 + 7y + 2y2 = 0

Solving
3 + 7y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + y)(1 + 2y) = 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 '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {-3, -0.5}