(3y-1)(5-y)=0

Solution for (3y-1)(5-y)=0 equation:

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

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

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

Combine like terms: 1y + 15y = 16y
(-5 + 16y + -3y2) = 0

Solving
-5 + 16y + -3y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(-5 + y)' equal to zero and attempt to solve:

Simplifying
-5 + y = 0

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

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

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

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

Simplifying
1 + -3y = 0

Solving
1 + -3y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3y = 0 + -1

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

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

Divide each side by '-3'.
y = 0.3333333333

Simplifying
y = 0.3333333333
Solution
y = {5, 0.3333333333}