y^2+3y=-2

Solution for y^2+3y=-2 equation:

Simplifying
y2 + 3y = -2

Reorder the terms:
3y + y2 = -2

Solving
3y + y2 = -2

Solving for variable 'y'.

Reorder the terms:
2 + 3y + y2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 3y + y2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
y = {-2, -1}