5y^2=-2y+3

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

Simplifying
5y2 = -2y + 3

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

Solving
5y2 = 3 + -2y

Solving for variable 'y'.

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

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

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

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

Factor a trinomial.
(-1 + -1y)(3 + -5y) = 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 '(3 + -5y)' equal to zero and attempt to solve:

Simplifying
3 + -5y = 0

Solving
3 + -5y = 0

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

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

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

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

Divide each side by '-5'.
y = 0.6

Simplifying
y = 0.6
Solution
y = {-1, 0.6}