y(y-5)-3y+15=0

Solution for y(y-5)-3y+15=0 equation:

Simplifying
y(y + -5) + -3y + 15 = 0

Reorder the terms:
y(-5 + y) + -3y + 15 = 0
(-5 * y + y * y) + -3y + 15 = 0
(-5y + y2) + -3y + 15 = 0

Reorder the terms:
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}