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

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

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

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

Multiply (-6 + 5y) * (3 + -1y)
(-6(3 + -1y) + 5y * (3 + -1y)) = 0
((3 * -6 + -1y * -6) + 5y * (3 + -1y)) = 0
((-18 + 6y) + 5y * (3 + -1y)) = 0
(-18 + 6y + (3 * 5y + -1y * 5y)) = 0
(-18 + 6y + (15y + -5y2)) = 0

Combine like terms: 6y + 15y = 21y
(-18 + 21y + -5y2) = 0

Solving
-18 + 21y + -5y2 = 0

Solving for variable 'y'.

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

Simplifying
6 + -5y = 0

Solving
6 + -5y = 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 + -5y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5y = 0 + -6
-5y = 0 + -6

Combine like terms: 0 + -6 = -6
-5y = -6

Divide each side by '-5'.
y = 1.2

Simplifying
y = 1.2
Solution
y = {3, 1.2}