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

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

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

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

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

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

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