5y^2=-3y+2

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

Simplifying
5y2 = -3y + 2

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

Solving
5y2 = 2 + -3y

Solving for variable 'y'.

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

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

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

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

Factor a trinomial.
(-1 + -1y)(2 + -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 '(2 + -5y)' equal to zero and attempt to solve:

Simplifying
2 + -5y = 0

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

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

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

Divide each side by '-5'.
y = 0.4

Simplifying
y = 0.4
Solution
y = {-1, 0.4}