0.12y(y-5)+0.04=0.20y-0.05(10)

Solution for 0.12y(y-5)+0.04=0.20y-0.05(10) equation:

Simplifying
0.12y(y + -5) + 0.04 = 0.20y + -0.05(10)

Reorder the terms:
0.12y(-5 + y) + 0.04 = 0.20y + -0.05(10)
(-5 * 0.12y + y * 0.12y) + 0.04 = 0.20y + -0.05(10)
(-0.6y + 0.12y2) + 0.04 = 0.20y + -0.05(10)

Reorder the terms:
0.04 + -0.6y + 0.12y2 = 0.20y + -0.05(10)

Multiply -0.05 * 10
0.04 + -0.6y + 0.12y2 = 0.20y + -0.5

Reorder the terms:
0.04 + -0.6y + 0.12y2 = -0.5 + 0.20y

Solving
0.04 + -0.6y + 0.12y2 = -0.5 + 0.20y

Solving for variable 'y'.

Reorder the terms:
0.04 + 0.5 + -0.6y + -0.20y + 0.12y2 = -0.5 + 0.20y + 0.5 + -0.20y

Combine like terms: 0.04 + 0.5 = 0.54
0.54 + -0.6y + -0.20y + 0.12y2 = -0.5 + 0.20y + 0.5 + -0.20y

Combine like terms: -0.6y + -0.20y = -0.8y
0.54 + -0.8y + 0.12y2 = -0.5 + 0.20y + 0.5 + -0.20y

Reorder the terms:
0.54 + -0.8y + 0.12y2 = -0.5 + 0.5 + 0.20y + -0.20y

Combine like terms: -0.5 + 0.5 = 0.0
0.54 + -0.8y + 0.12y2 = 0.0 + 0.20y + -0.20y
0.54 + -0.8y + 0.12y2 = 0.20y + -0.20y

Combine like terms: 0.20y + -0.20y = 0.00
0.54 + -0.8y + 0.12y2 = 0.00

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

Divide each side by '0.12'.
4.5 + -6.666666667y + y2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -6.666666667y + -4.5 + y2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -6.666666667y + y2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -6.666666667y + y2 = 0 + -4.5
-6.666666667y + y2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-6.666666667y + y2 = -4.5

The y term is -6.666666667y.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667y + 11.11111112 + y2 = -4.5 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667y + y2 = -4.5 + 11.11111112

Combine like terms: -4.5 + 11.11111112 = 6.61111112
11.11111112 + -6.666666667y + y2 = 6.61111112

Factor a perfect square on the left side:
(y + -3.333333334)(y + -3.333333334) = 6.61111112

Calculate the square root of the right side: 2.571208105

Break this problem into two subproblems by setting 
(y + -3.333333334) equal to 2.571208105 and -2.571208105.

Subproblem 1
y + -3.333333334 = 2.571208105

Simplifying
y + -3.333333334 = 2.571208105

Reorder the terms:
-3.333333334 + y = 2.571208105

Solving
-3.333333334 + y = 2.571208105

Solving for variable 'y'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + y = 2.571208105 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + y = 2.571208105 + 3.333333334
y = 2.571208105 + 3.333333334

Combine like terms: 2.571208105 + 3.333333334 = 5.904541439
y = 5.904541439

Simplifying
y = 5.904541439

Subproblem 2
y + -3.333333334 = -2.571208105

Simplifying
y + -3.333333334 = -2.571208105

Reorder the terms:
-3.333333334 + y = -2.571208105

Solving
-3.333333334 + y = -2.571208105

Solving for variable 'y'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + y = -2.571208105 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + y = -2.571208105 + 3.333333334
y = -2.571208105 + 3.333333334

Combine like terms: -2.571208105 + 3.333333334 = 0.762125229
y = 0.762125229

Simplifying
y = 0.762125229

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.904541439, 0.762125229}