8y(5y-15)=36

Solution for 8y(5y-15)=36 equation:

Simplifying
8y(5y + -15) = 36

Reorder the terms:
8y(-15 + 5y) = 36
(-15 * 8y + 5y * 8y) = 36
(-120y + 40y2) = 36

Solving
-120y + 40y2 = 36

Solving for variable 'y'.

Reorder the terms:
-36 + -120y + 40y2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + -120y + 40y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -30y + 10y2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-9 + -30y + 10y2)' equal to zero and attempt to solve:

Simplifying
-9 + -30y + 10y2 = 0

Solving
-9 + -30y + 10y2 = 0

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

Divide each side by '10'.
-0.9 + -3y + y2 = 0.0

Move the constant term to the right:

Add '0.9' to each side of the equation.
-0.9 + -3y + 0.9 + y2 = 0.0 + 0.9

Reorder the terms:
-0.9 + 0.9 + -3y + y2 = 0.0 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + -3y + y2 = 0.0 + 0.9
-3y + y2 = 0.0 + 0.9

Combine like terms: 0.0 + 0.9 = 0.9
-3y + y2 = 0.9

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 0.9 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 0.9 + 2.25

Combine like terms: 0.9 + 2.25 = 3.15
2.25 + -3y + y2 = 3.15

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 3.15

Calculate the square root of the right side: 1.774823935

Break this problem into two subproblems by setting 
(y + -1.5) equal to 1.774823935 and -1.774823935.

Subproblem 1
y + -1.5 = 1.774823935

Simplifying
y + -1.5 = 1.774823935

Reorder the terms:
-1.5 + y = 1.774823935

Solving
-1.5 + y = 1.774823935

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 1.774823935 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 1.774823935 + 1.5
y = 1.774823935 + 1.5

Combine like terms: 1.774823935 + 1.5 = 3.274823935
y = 3.274823935

Simplifying
y = 3.274823935

Subproblem 2
y + -1.5 = -1.774823935

Simplifying
y + -1.5 = -1.774823935

Reorder the terms:
-1.5 + y = -1.774823935

Solving
-1.5 + y = -1.774823935

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -1.774823935 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -1.774823935 + 1.5
y = -1.774823935 + 1.5

Combine like terms: -1.774823935 + 1.5 = -0.274823935
y = -0.274823935

Simplifying
y = -0.274823935

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.274823935, -0.274823935}
Solution
y = {3.274823935, -0.274823935}