9y(6-5y)3=y-2(3y+9)

Solution for 9y(6-5y)3=y-2(3y+9) equation:

Simplifying
9y(6 + -5y) * 3 = y + -2(3y + 9)

Reorder the terms for easier multiplication:
9 * 3y(6 + -5y) = y + -2(3y + 9)

Multiply 9 * 3
27y(6 + -5y) = y + -2(3y + 9)
(6 * 27y + -5y * 27y) = y + -2(3y + 9)
(162y + -135y2) = y + -2(3y + 9)

Reorder the terms:
162y + -135y2 = y + -2(9 + 3y)
162y + -135y2 = y + (9 * -2 + 3y * -2)
162y + -135y2 = y + (-18 + -6y)

Reorder the terms:
162y + -135y2 = -18 + y + -6y

Combine like terms: y + -6y = -5y
162y + -135y2 = -18 + -5y

Solving
162y + -135y2 = -18 + -5y

Solving for variable 'y'.

Reorder the terms:
18 + 162y + 5y + -135y2 = -18 + -5y + 18 + 5y

Combine like terms: 162y + 5y = 167y
18 + 167y + -135y2 = -18 + -5y + 18 + 5y

Reorder the terms:
18 + 167y + -135y2 = -18 + 18 + -5y + 5y

Combine like terms: -18 + 18 = 0
18 + 167y + -135y2 = 0 + -5y + 5y
18 + 167y + -135y2 = -5y + 5y

Combine like terms: -5y + 5y = 0
18 + 167y + -135y2 = 0

Begin completing the square.  Divide all terms by
-135 the coefficient of the squared term: 

Divide each side by '-135'.
-0.1333333333 + -1.237037037y + y2 = 0

Move the constant term to the right:

Add '0.1333333333' to each side of the equation.
-0.1333333333 + -1.237037037y + 0.1333333333 + y2 = 0 + 0.1333333333

Reorder the terms:
-0.1333333333 + 0.1333333333 + -1.237037037y + y2 = 0 + 0.1333333333

Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000
0.0000000000 + -1.237037037y + y2 = 0 + 0.1333333333
-1.237037037y + y2 = 0 + 0.1333333333

Combine like terms: 0 + 0.1333333333 = 0.1333333333
-1.237037037y + y2 = 0.1333333333

The y term is -1.237037037y.  Take half its coefficient (-0.6185185185).
Square it (0.3825651577) and add it to both sides.

Add '0.3825651577' to each side of the equation.
-1.237037037y + 0.3825651577 + y2 = 0.1333333333 + 0.3825651577

Reorder the terms:
0.3825651577 + -1.237037037y + y2 = 0.1333333333 + 0.3825651577

Combine like terms: 0.1333333333 + 0.3825651577 = 0.515898491
0.3825651577 + -1.237037037y + y2 = 0.515898491

Factor a perfect square on the left side:
(y + -0.6185185185)(y + -0.6185185185) = 0.515898491

Calculate the square root of the right side: 0.71826074

Break this problem into two subproblems by setting 
(y + -0.6185185185) equal to 0.71826074 and -0.71826074.

Subproblem 1
y + -0.6185185185 = 0.71826074

Simplifying
y + -0.6185185185 = 0.71826074

Reorder the terms:
-0.6185185185 + y = 0.71826074

Solving
-0.6185185185 + y = 0.71826074

Solving for variable 'y'.

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

Add '0.6185185185' to each side of the equation.
-0.6185185185 + 0.6185185185 + y = 0.71826074 + 0.6185185185

Combine like terms: -0.6185185185 + 0.6185185185 = 0.0000000000
0.0000000000 + y = 0.71826074 + 0.6185185185
y = 0.71826074 + 0.6185185185

Combine like terms: 0.71826074 + 0.6185185185 = 1.3367792585
y = 1.3367792585

Simplifying
y = 1.3367792585

Subproblem 2
y + -0.6185185185 = -0.71826074

Simplifying
y + -0.6185185185 = -0.71826074

Reorder the terms:
-0.6185185185 + y = -0.71826074

Solving
-0.6185185185 + y = -0.71826074

Solving for variable 'y'.

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

Add '0.6185185185' to each side of the equation.
-0.6185185185 + 0.6185185185 + y = -0.71826074 + 0.6185185185

Combine like terms: -0.6185185185 + 0.6185185185 = 0.0000000000
0.0000000000 + y = -0.71826074 + 0.6185185185
y = -0.71826074 + 0.6185185185

Combine like terms: -0.71826074 + 0.6185185185 = -0.0997422215
y = -0.0997422215

Simplifying
y = -0.0997422215

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.3367792585, -0.0997422215}