(3y-2)(3-y)=0

Solution for (3y-2)(3-y)=0 equation:

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

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

Multiply (-2 + 3y) * (3 + -1y)
(-2(3 + -1y) + 3y * (3 + -1y)) = 0
((3 * -2 + -1y * -2) + 3y * (3 + -1y)) = 0
((-6 + 2y) + 3y * (3 + -1y)) = 0
(-6 + 2y + (3 * 3y + -1y * 3y)) = 0
(-6 + 2y + (9y + -3y2)) = 0

Combine like terms: 2y + 9y = 11y
(-6 + 11y + -3y2) = 0

Solving
-6 + 11y + -3y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(-3 + y)' equal to zero and attempt to solve:

Simplifying
-3 + y = 0

Solving
-3 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + y = 0 + 3
y = 0 + 3

Combine like terms: 0 + 3 = 3
y = 3

Simplifying
y = 3
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 = {3, 0.6666666667}