-3y=2y^2+1

Solution for -3y=2y^2+1 equation:

Simplifying
-3y = 2y2 + 1

Reorder the terms:
-3y = 1 + 2y2

Solving
-3y = 1 + 2y2

Solving for variable 'y'.

Reorder the terms:
-1 + -3y + -2y2 = 1 + 2y2 + -1 + -2y2

Reorder the terms:
-1 + -3y + -2y2 = 1 + -1 + 2y2 + -2y2

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

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

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

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

Ignore the factor -1.
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}