0.10(y-2)0.18y=0.20y-0.1

Solution for 0.10(y-2)0.18y=0.20y-0.1 equation:

Simplifying
0.10(y + -2) * 0.18y = 0.20y + -0.1

Reorder the terms:
0.10(-2 + y) * 0.18y = 0.20y + -0.1

Reorder the terms for easier multiplication:
0.10 * 0.18y(-2 + y) = 0.20y + -0.1

Multiply 0.10 * 0.18
0.018y(-2 + y) = 0.20y + -0.1
(-2 * 0.018y + y * 0.018y) = 0.20y + -0.1
(-0.036y + 0.018y2) = 0.20y + -0.1

Reorder the terms:
-0.036y + 0.018y2 = -0.1 + 0.20y

Solving
-0.036y + 0.018y2 = -0.1 + 0.20y

Solving for variable 'y'.

Reorder the terms:
0.1 + -0.036y + -0.20y + 0.018y2 = -0.1 + 0.20y + 0.1 + -0.20y

Combine like terms: -0.036y + -0.20y = -0.236y
0.1 + -0.236y + 0.018y2 = -0.1 + 0.20y + 0.1 + -0.20y

Reorder the terms:
0.1 + -0.236y + 0.018y2 = -0.1 + 0.1 + 0.20y + -0.20y

Combine like terms: -0.1 + 0.1 = 0.0
0.1 + -0.236y + 0.018y2 = 0.0 + 0.20y + -0.20y
0.1 + -0.236y + 0.018y2 = 0.20y + -0.20y

Combine like terms: 0.20y + -0.20y = 0.00
0.1 + -0.236y + 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'.
5.555555556 + -13.11111111y + y2 = 0

Move the constant term to the right:

Add '-5.555555556' to each side of the equation.
5.555555556 + -13.11111111y + -5.555555556 + y2 = 0 + -5.555555556

Reorder the terms:
5.555555556 + -5.555555556 + -13.11111111y + y2 = 0 + -5.555555556

Combine like terms: 5.555555556 + -5.555555556 = 0.000000000
0.000000000 + -13.11111111y + y2 = 0 + -5.555555556
-13.11111111y + y2 = 0 + -5.555555556

Combine like terms: 0 + -5.555555556 = -5.555555556
-13.11111111y + y2 = -5.555555556

The y term is -13.11111111y.  Take half its coefficient (-6.555555555).
Square it (42.97530863) and add it to both sides.

Add '42.97530863' to each side of the equation.
-13.11111111y + 42.97530863 + y2 = -5.555555556 + 42.97530863

Reorder the terms:
42.97530863 + -13.11111111y + y2 = -5.555555556 + 42.97530863

Combine like terms: -5.555555556 + 42.97530863 = 37.419753074
42.97530863 + -13.11111111y + y2 = 37.419753074

Factor a perfect square on the left side:
(y + -6.555555555)(y + -6.555555555) = 37.419753074

Calculate the square root of the right side: 6.117168714

Break this problem into two subproblems by setting 
(y + -6.555555555) equal to 6.117168714 and -6.117168714.

Subproblem 1
y + -6.555555555 = 6.117168714

Simplifying
y + -6.555555555 = 6.117168714

Reorder the terms:
-6.555555555 + y = 6.117168714

Solving
-6.555555555 + y = 6.117168714

Solving for variable 'y'.

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

Add '6.555555555' to each side of the equation.
-6.555555555 + 6.555555555 + y = 6.117168714 + 6.555555555

Combine like terms: -6.555555555 + 6.555555555 = 0.000000000
0.000000000 + y = 6.117168714 + 6.555555555
y = 6.117168714 + 6.555555555

Combine like terms: 6.117168714 + 6.555555555 = 12.672724269
y = 12.672724269

Simplifying
y = 12.672724269

Subproblem 2
y + -6.555555555 = -6.117168714

Simplifying
y + -6.555555555 = -6.117168714

Reorder the terms:
-6.555555555 + y = -6.117168714

Solving
-6.555555555 + y = -6.117168714

Solving for variable 'y'.

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

Add '6.555555555' to each side of the equation.
-6.555555555 + 6.555555555 + y = -6.117168714 + 6.555555555

Combine like terms: -6.555555555 + 6.555555555 = 0.000000000
0.000000000 + y = -6.117168714 + 6.555555555
y = -6.117168714 + 6.555555555

Combine like terms: -6.117168714 + 6.555555555 = 0.438386841
y = 0.438386841

Simplifying
y = 0.438386841

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {12.672724269, 0.438386841}