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.
(-2 + -1y)(1 + -3y) = 0

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

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

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

Divide each side by '-1'.
y = -2

Simplifying
y = -2
Subproblem 2
Set the factor '(1 + -3y)' equal to zero and attempt to solve:

Simplifying
1 + -3y = 0

Solving
1 + -3y = 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 + -3y = 0 + -1

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

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

Divide each side by '-3'.
y = 0.3333333333

Simplifying
y = 0.3333333333
Solution
y = {-2, 0.3333333333}