(1-Y)(3Y-2)=0

Solution for (1-Y)(3Y-2)=0 equation:

Simplifying
(1 + -1Y)(3Y + -2) = 0

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

Multiply (1 + -1Y) * (-2 + 3Y)
(1(-2 + 3Y) + -1Y * (-2 + 3Y)) = 0
((-2 * 1 + 3Y * 1) + -1Y * (-2 + 3Y)) = 0
((-2 + 3Y) + -1Y * (-2 + 3Y)) = 0
(-2 + 3Y + (-2 * -1Y + 3Y * -1Y)) = 0
(-2 + 3Y + (2Y + -3Y2)) = 0

Combine like terms: 3Y + 2Y = 5Y
(-2 + 5Y + -3Y2) = 0

Solving
-2 + 5Y + -3Y2 = 0

Solving for variable 'Y'.

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}