-3y(y-5)=15

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

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

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

Solving
15y + -3y2 = 15

Solving for variable 'y'.

Reorder the terms:
-15 + 15y + -3y2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 15y + -3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 5y + -1y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + 5y + -1y2)' equal to zero and attempt to solve:

Simplifying
-5 + 5y + -1y2 = 0

Solving
-5 + 5y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -5y + y2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -5y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + -5y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -5y + y2 = 0 + -5
-5y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
-5y + y2 = -5

The y term is -5y.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5y + 6.25 + y2 = -5 + 6.25

Reorder the terms:
6.25 + -5y + y2 = -5 + 6.25

Combine like terms: -5 + 6.25 = 1.25
6.25 + -5y + y2 = 1.25

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(y + -2.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
y + -2.5 = 1.118033989

Simplifying
y + -2.5 = 1.118033989

Reorder the terms:
-2.5 + y = 1.118033989

Solving
-2.5 + y = 1.118033989

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = 1.118033989 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = 1.118033989 + 2.5
y = 1.118033989 + 2.5

Combine like terms: 1.118033989 + 2.5 = 3.618033989
y = 3.618033989

Simplifying
y = 3.618033989

Subproblem 2
y + -2.5 = -1.118033989

Simplifying
y + -2.5 = -1.118033989

Reorder the terms:
-2.5 + y = -1.118033989

Solving
-2.5 + y = -1.118033989

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = -1.118033989 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = -1.118033989 + 2.5
y = -1.118033989 + 2.5

Combine like terms: -1.118033989 + 2.5 = 1.381966011
y = 1.381966011

Simplifying
y = 1.381966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.618033989, 1.381966011}
Solution
y = {3.618033989, 1.381966011}