.10(y-9)0.18y=0.08-0.01(20)

Solution for .10(y-9)0.18y=0.08-0.01(20) equation:

Simplifying
0.10(y + -9) * 0.18y = 0.08 + -0.01(20)

Reorder the terms:
0.10(-9 + y) * 0.18y = 0.08 + -0.01(20)

Reorder the terms for easier multiplication:
0.10 * 0.18y(-9 + y) = 0.08 + -0.01(20)

Multiply 0.10 * 0.18
0.018y(-9 + y) = 0.08 + -0.01(20)
(-9 * 0.018y + y * 0.018y) = 0.08 + -0.01(20)
(-0.162y + 0.018y2) = 0.08 + -0.01(20)

Multiply -0.01 * 20
-0.162y + 0.018y2 = 0.08 + -0.2

Combine like terms: 0.08 + -0.2 = -0.12
-0.162y + 0.018y2 = -0.12

Solving
-0.162y + 0.018y2 = -0.12

Solving for variable 'y'.

Reorder the terms:
0.12 + -0.162y + 0.018y2 = -0.12 + 0.12

Combine like terms: -0.12 + 0.12 = 0.00
0.12 + -0.162y + 0.018y2 = 0.00

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

Divide each side by '0.018'.
6.666666667 + -9y + y2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -9y + -6.666666667 + y2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -9y + y2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -9y + y2 = 0 + -6.666666667
-9y + y2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-9y + y2 = -6.666666667

The y term is -9y.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9y + 20.25 + y2 = -6.666666667 + 20.25

Reorder the terms:
20.25 + -9y + y2 = -6.666666667 + 20.25

Combine like terms: -6.666666667 + 20.25 = 13.583333333
20.25 + -9y + y2 = 13.583333333

Factor a perfect square on the left side:
(y + -4.5)(y + -4.5) = 13.583333333

Calculate the square root of the right side: 3.685557398

Break this problem into two subproblems by setting 
(y + -4.5) equal to 3.685557398 and -3.685557398.

Subproblem 1
y + -4.5 = 3.685557398

Simplifying
y + -4.5 = 3.685557398

Reorder the terms:
-4.5 + y = 3.685557398

Solving
-4.5 + y = 3.685557398

Solving for variable 'y'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + y = 3.685557398 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + y = 3.685557398 + 4.5
y = 3.685557398 + 4.5

Combine like terms: 3.685557398 + 4.5 = 8.185557398
y = 8.185557398

Simplifying
y = 8.185557398

Subproblem 2
y + -4.5 = -3.685557398

Simplifying
y + -4.5 = -3.685557398

Reorder the terms:
-4.5 + y = -3.685557398

Solving
-4.5 + y = -3.685557398

Solving for variable 'y'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + y = -3.685557398 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + y = -3.685557398 + 4.5
y = -3.685557398 + 4.5

Combine like terms: -3.685557398 + 4.5 = 0.814442602
y = 0.814442602

Simplifying
y = 0.814442602

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {8.185557398, 0.814442602}