-3y^2+5y=2

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

Simplifying
-3y2 + 5y = 2

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

Solving
5y + -3y2 = 2

Solving for variable 'y'.

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

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

Factor a trinomial.
(-1 + y)(2 + -3y) = 0

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 '(2 + -3y)' equal to zero and attempt to solve:

Simplifying
2 + -3y = 0

Solving
2 + -3y = 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 + -3y = 0 + -2

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

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

Divide each side by '-3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Solution
y = {1, 0.6666666667}