2y=3y^2-5

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

Simplifying
2y = 3y2 + -5

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

Solving
2y = -5 + 3y2

Solving for variable 'y'.

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

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

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

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

Factor a trinomial.
(5 + -3y)(1 + y) = 0

Subproblem 1
Set the factor '(5 + -3y)' equal to zero and attempt to solve:

Simplifying
5 + -3y = 0

Solving
5 + -3y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -3y = 0 + -5

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

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

Divide each side by '-3'.
y = 1.666666667

Simplifying
y = 1.666666667
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 = {1.666666667, -1}