(3y-5)(6-y)=0

Solution for (3y-5)(6-y)=0 equation:

Simplifying
(3y + -5)(6 + -1y) = 0

Reorder the terms:
(-5 + 3y)(6 + -1y) = 0

Multiply (-5 + 3y) * (6 + -1y)
(-5(6 + -1y) + 3y * (6 + -1y)) = 0
((6 * -5 + -1y * -5) + 3y * (6 + -1y)) = 0
((-30 + 5y) + 3y * (6 + -1y)) = 0
(-30 + 5y + (6 * 3y + -1y * 3y)) = 0
(-30 + 5y + (18y + -3y2)) = 0

Combine like terms: 5y + 18y = 23y
(-30 + 23y + -3y2) = 0

Solving
-30 + 23y + -3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + y)(5 + -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 '(5 + -3y)' equal to zero and attempt to solve:

Simplifying
5 + -3y = 0

Solving
5 + -3y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3y = 0 + -5
-3y = 0 + -5

Combine like terms: 0 + -5 = -5
-3y = -5

Divide each side by '-3'.
y = 1.666666667

Simplifying
y = 1.666666667
Solution
y = {6, 1.666666667}