(y^2+2y)+(3y^2+4y+2)=0

Solution for (y^2+2y)+(3y^2+4y+2)=0 equation:

Simplifying
(y2 + 2y) + (3y2 + 4y + 2) = 0

Reorder the terms:
(2y + y2) + (3y2 + 4y + 2) = 0

Remove parenthesis around (2y + y2)
2y + y2 + (3y2 + 4y + 2) = 0

Reorder the terms:
2y + y2 + (2 + 4y + 3y2) = 0

Remove parenthesis around (2 + 4y + 3y2)
2y + y2 + 2 + 4y + 3y2 = 0

Reorder the terms:
2 + 2y + 4y + y2 + 3y2 = 0

Combine like terms: 2y + 4y = 6y
2 + 6y + y2 + 3y2 = 0

Combine like terms: y2 + 3y2 = 4y2
2 + 6y + 4y2 = 0

Solving
2 + 6y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 3y + 2y2) = 0

Factor a trinomial.
2((1 + y)(1 + 2y)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-1, -0.5}