2y^2=5+3y

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

Simplifying
2y2 = 5 + 3y

Solving
2y2 = 5 + 3y

Solving for variable 'y'.

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

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

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

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

Factor a trinomial.
(-1 + -1y)(5 + -2y) = 0

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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 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 + -1y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1y = 0 + 1
-1y = 0 + 1

Combine like terms: 0 + 1 = 1
-1y = 1

Divide each side by '-1'.
y = -1

Simplifying
y = -1
Subproblem 2
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 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 + -2y = 0 + -5

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

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

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {-1, 2.5}