0.10y(y-7)+0.12y=0.20y-0.03(20)

Solution for 0.10y(y-7)+0.12y=0.20y-0.03(20) equation:

Simplifying
0.10y(y + -7) + 0.12y = 0.20y + -0.03(20)

Reorder the terms:
0.10y(-7 + y) + 0.12y = 0.20y + -0.03(20)
(-7 * 0.10y + y * 0.10y) + 0.12y = 0.20y + -0.03(20)
(-0.7y + 0.10y2) + 0.12y = 0.20y + -0.03(20)

Reorder the terms:
-0.7y + 0.12y + 0.10y2 = 0.20y + -0.03(20)

Combine like terms: -0.7y + 0.12y = -0.58y
-0.58y + 0.10y2 = 0.20y + -0.03(20)

Multiply -0.03 * 20
-0.58y + 0.10y2 = 0.20y + -0.6

Reorder the terms:
-0.58y + 0.10y2 = -0.6 + 0.20y

Solving
-0.58y + 0.10y2 = -0.6 + 0.20y

Solving for variable 'y'.

Reorder the terms:
0.6 + -0.58y + -0.20y + 0.10y2 = -0.6 + 0.20y + 0.6 + -0.20y

Combine like terms: -0.58y + -0.20y = -0.78y
0.6 + -0.78y + 0.10y2 = -0.6 + 0.20y + 0.6 + -0.20y

Reorder the terms:
0.6 + -0.78y + 0.10y2 = -0.6 + 0.6 + 0.20y + -0.20y

Combine like terms: -0.6 + 0.6 = 0.0
0.6 + -0.78y + 0.10y2 = 0.0 + 0.20y + -0.20y
0.6 + -0.78y + 0.10y2 = 0.20y + -0.20y

Combine like terms: 0.20y + -0.20y = 0.00
0.6 + -0.78y + 0.10y2 = 0.00

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

Divide each side by '0.10'.
6 + -7.8y + y2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -7.8y + -6 + y2 = 0 + -6

Reorder the terms:
6 + -6 + -7.8y + y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7.8y + y2 = 0 + -6
-7.8y + y2 = 0 + -6

Combine like terms: 0 + -6 = -6
-7.8y + y2 = -6

The y term is -7.8y.  Take half its coefficient (-3.9).
Square it (15.21) and add it to both sides.

Add '15.21' to each side of the equation.
-7.8y + 15.21 + y2 = -6 + 15.21

Reorder the terms:
15.21 + -7.8y + y2 = -6 + 15.21

Combine like terms: -6 + 15.21 = 9.21
15.21 + -7.8y + y2 = 9.21

Factor a perfect square on the left side:
(y + -3.9)(y + -3.9) = 9.21

Calculate the square root of the right side: 3.034798181

Break this problem into two subproblems by setting 
(y + -3.9) equal to 3.034798181 and -3.034798181.

Subproblem 1
y + -3.9 = 3.034798181

Simplifying
y + -3.9 = 3.034798181

Reorder the terms:
-3.9 + y = 3.034798181

Solving
-3.9 + y = 3.034798181

Solving for variable 'y'.

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

Add '3.9' to each side of the equation.
-3.9 + 3.9 + y = 3.034798181 + 3.9

Combine like terms: -3.9 + 3.9 = 0.0
0.0 + y = 3.034798181 + 3.9
y = 3.034798181 + 3.9

Combine like terms: 3.034798181 + 3.9 = 6.934798181
y = 6.934798181

Simplifying
y = 6.934798181

Subproblem 2
y + -3.9 = -3.034798181

Simplifying
y + -3.9 = -3.034798181

Reorder the terms:
-3.9 + y = -3.034798181

Solving
-3.9 + y = -3.034798181

Solving for variable 'y'.

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

Add '3.9' to each side of the equation.
-3.9 + 3.9 + y = -3.034798181 + 3.9

Combine like terms: -3.9 + 3.9 = 0.0
0.0 + y = -3.034798181 + 3.9
y = -3.034798181 + 3.9

Combine like terms: -3.034798181 + 3.9 = 0.865201819
y = 0.865201819

Simplifying
y = 0.865201819

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.934798181, 0.865201819}