3y^2=-5y-2

Solution for 3y^2=-5y-2 equation:

Simplifying
3y2 = -5y + -2

Reorder the terms:
3y2 = -2 + -5y

Solving
3y2 = -2 + -5y

Solving for variable 'y'.

Reorder the terms:
2 + 5y + 3y2 = -2 + -5y + 2 + 5y

Reorder the terms:
2 + 5y + 3y2 = -2 + 2 + -5y + 5y

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

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

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

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 '(2 + 3y)' equal to zero and attempt to solve:

Simplifying
2 + 3y = 0

Solving
2 + 3y = 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 + 3y = 0 + -2

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

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

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Solution
y = {-1, -0.6666666667}