3Y^2=Y+2

Solution for 3Y^2=Y+2 equation:

Simplifying
3Y2 = Y + 2

Reorder the terms:
3Y2 = 2 + Y

Solving
3Y2 = 2 + Y

Solving for variable 'Y'.

Reorder the terms:
-2 + -1Y + 3Y2 = 2 + Y + -2 + -1Y

Reorder the terms:
-2 + -1Y + 3Y2 = 2 + -2 + Y + -1Y

Combine like terms: 2 + -2 = 0
-2 + -1Y + 3Y2 = 0 + Y + -1Y
-2 + -1Y + 3Y2 = Y + -1Y

Combine like terms: Y + -1Y = 0
-2 + -1Y + 3Y2 = 0

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

Subproblem 1
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
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 = {-0.6666666667, 1}