3Y^2+2Y-1=0

Solution for 3Y^2+2Y-1=0 equation:

Simplifying
3Y2 + 2Y + -1 = 0

Reorder the terms:
-1 + 2Y + 3Y2 = 0

Solving
-1 + 2Y + 3Y2 = 0

Solving for variable 'Y'.

Factor a trinomial.
(-1 + -1Y)(1 + -3Y) = 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 '(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 = {-1, 0.3333333333}