(Y-5)(Y-3)=0

Solution for (Y-5)(Y-3)=0 equation:

Simplifying
(Y + -5)(Y + -3) = 0

Reorder the terms:
(-5 + Y)(Y + -3) = 0

Reorder the terms:
(-5 + Y)(-3 + Y) = 0

Multiply (-5 + Y) * (-3 + Y)
(-5(-3 + Y) + Y(-3 + Y)) = 0
((-3 * -5 + Y * -5) + Y(-3 + Y)) = 0
((15 + -5Y) + Y(-3 + Y)) = 0
(15 + -5Y + (-3 * Y + Y * Y)) = 0
(15 + -5Y + (-3Y + Y2)) = 0

Combine like terms: -5Y + -3Y = -8Y
(15 + -8Y + Y2) = 0

Solving
15 + -8Y + Y2 = 0

Solving for variable 'Y'.

Factor a trinomial.
(3 + -1Y)(5 + -1Y) = 0

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

Simplifying
3 + -1Y = 0

Solving
3 + -1Y = 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 + -1Y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1Y = 0 + -3
-1Y = 0 + -3

Combine like terms: 0 + -3 = -3
-1Y = -3

Divide each side by '-1'.
Y = 3

Simplifying
Y = 3
Subproblem 2
Set the factor '(5 + -1Y)' equal to zero and attempt to solve:

Simplifying
5 + -1Y = 0

Solving
5 + -1Y = 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 + -1Y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1Y = 0 + -5
-1Y = 0 + -5

Combine like terms: 0 + -5 = -5
-1Y = -5

Divide each side by '-1'.
Y = 5

Simplifying
Y = 5
Solution
Y = {3, 5}