-2y(y+12)=y-9

Solution for -2y(y+12)=y-9 equation:

Simplifying
-2y(y + 12) = y + -9

Reorder the terms:
-2y(12 + y) = y + -9
(12 * -2y + y * -2y) = y + -9
(-24y + -2y2) = y + -9

Reorder the terms:
-24y + -2y2 = -9 + y

Solving
-24y + -2y2 = -9 + y

Solving for variable 'y'.

Reorder the terms:
9 + -24y + -1y + -2y2 = -9 + y + 9 + -1y

Combine like terms: -24y + -1y = -25y
9 + -25y + -2y2 = -9 + y + 9 + -1y

Reorder the terms:
9 + -25y + -2y2 = -9 + 9 + y + -1y

Combine like terms: -9 + 9 = 0
9 + -25y + -2y2 = 0 + y + -1y
9 + -25y + -2y2 = y + -1y

Combine like terms: y + -1y = 0
9 + -25y + -2y2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-4.5 + 12.5y + y2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 12.5y + 4.5 + y2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 12.5y + y2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 12.5y + y2 = 0 + 4.5
12.5y + y2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
12.5y + y2 = 4.5

The y term is 12.5y.  Take half its coefficient (6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
12.5y + 39.0625 + y2 = 4.5 + 39.0625

Reorder the terms:
39.0625 + 12.5y + y2 = 4.5 + 39.0625

Combine like terms: 4.5 + 39.0625 = 43.5625
39.0625 + 12.5y + y2 = 43.5625

Factor a perfect square on the left side:
(y + 6.25)(y + 6.25) = 43.5625

Calculate the square root of the right side: 6.600189391

Break this problem into two subproblems by setting 
(y + 6.25) equal to 6.600189391 and -6.600189391.

Subproblem 1
y + 6.25 = 6.600189391

Simplifying
y + 6.25 = 6.600189391

Reorder the terms:
6.25 + y = 6.600189391

Solving
6.25 + y = 6.600189391

Solving for variable 'y'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + y = 6.600189391 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + y = 6.600189391 + -6.25
y = 6.600189391 + -6.25

Combine like terms: 6.600189391 + -6.25 = 0.350189391
y = 0.350189391

Simplifying
y = 0.350189391

Subproblem 2
y + 6.25 = -6.600189391

Simplifying
y + 6.25 = -6.600189391

Reorder the terms:
6.25 + y = -6.600189391

Solving
6.25 + y = -6.600189391

Solving for variable 'y'.

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

Add '-6.25' to each side of the equation.
6.25 + -6.25 + y = -6.600189391 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + y = -6.600189391 + -6.25
y = -6.600189391 + -6.25

Combine like terms: -6.600189391 + -6.25 = -12.850189391
y = -12.850189391

Simplifying
y = -12.850189391

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.350189391, -12.850189391}