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

Solution for (6-y)(3y-2)=0 equation:

Simplifying
(6 + -1y)(3y + -2) = 0

Reorder the terms:
(6 + -1y)(-2 + 3y) = 0

Multiply (6 + -1y) * (-2 + 3y)
(6(-2 + 3y) + -1y * (-2 + 3y)) = 0
((-2 * 6 + 3y * 6) + -1y * (-2 + 3y)) = 0
((-12 + 18y) + -1y * (-2 + 3y)) = 0
(-12 + 18y + (-2 * -1y + 3y * -1y)) = 0
(-12 + 18y + (2y + -3y2)) = 0

Combine like terms: 18y + 2y = 20y
(-12 + 20y + -3y2) = 0

Solving
-12 + 20y + -3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + y)(2 + -3y) = 0

Subproblem 1
Set the factor '(-6 + y)' equal to zero and attempt to solve:

Simplifying
-6 + y = 0

Solving
-6 + y = 0

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

Add '6' to each side of the equation.
-6 + 6 + y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + y = 0 + 6
y = 0 + 6

Combine like terms: 0 + 6 = 6
y = 6

Simplifying
y = 6
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 = {6, 0.6666666667}