3y^2=2y+1

Solution for 3y^2=2y+1 equation:

Simplifying
3y2 = 2y + 1

Reorder the terms:
3y2 = 1 + 2y

Solving
3y2 = 1 + 2y

Solving for variable 'y'.

Reorder the terms:
-1 + -2y + 3y2 = 1 + 2y + -1 + -2y

Reorder the terms:
-1 + -2y + 3y2 = 1 + -1 + 2y + -2y

Combine like terms: 1 + -1 = 0
-1 + -2y + 3y2 = 0 + 2y + -2y
-1 + -2y + 3y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-1 + -2y + 3y2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
y = {-0.3333333333, 1}