2y+5y(2-y)=3-5y

Solution for 2y+5y(2-y)=3-5y equation:

Simplifying
2y + 5y(2 + -1y) = 3 + -5y
2y + (2 * 5y + -1y * 5y) = 3 + -5y
2y + (10y + -5y2) = 3 + -5y

Combine like terms: 2y + 10y = 12y
12y + -5y2 = 3 + -5y

Solving
12y + -5y2 = 3 + -5y

Solving for variable 'y'.

Reorder the terms:
-3 + 12y + 5y + -5y2 = 3 + -5y + -3 + 5y

Combine like terms: 12y + 5y = 17y
-3 + 17y + -5y2 = 3 + -5y + -3 + 5y

Reorder the terms:
-3 + 17y + -5y2 = 3 + -3 + -5y + 5y

Combine like terms: 3 + -3 = 0
-3 + 17y + -5y2 = 0 + -5y + 5y
-3 + 17y + -5y2 = -5y + 5y

Combine like terms: -5y + 5y = 0
-3 + 17y + -5y2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.6 + -3.4y + y2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -3.4y + -0.6 + y2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -3.4y + y2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -3.4y + y2 = 0 + -0.6
-3.4y + y2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-3.4y + y2 = -0.6

The y term is -3.4y.  Take half its coefficient (-1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
-3.4y + 2.89 + y2 = -0.6 + 2.89

Reorder the terms:
2.89 + -3.4y + y2 = -0.6 + 2.89

Combine like terms: -0.6 + 2.89 = 2.29
2.89 + -3.4y + y2 = 2.29

Factor a perfect square on the left side:
(y + -1.7)(y + -1.7) = 2.29

Calculate the square root of the right side: 1.513274595

Break this problem into two subproblems by setting 
(y + -1.7) equal to 1.513274595 and -1.513274595.

Subproblem 1
y + -1.7 = 1.513274595

Simplifying
y + -1.7 = 1.513274595

Reorder the terms:
-1.7 + y = 1.513274595

Solving
-1.7 + y = 1.513274595

Solving for variable 'y'.

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

Add '1.7' to each side of the equation.
-1.7 + 1.7 + y = 1.513274595 + 1.7

Combine like terms: -1.7 + 1.7 = 0.0
0.0 + y = 1.513274595 + 1.7
y = 1.513274595 + 1.7

Combine like terms: 1.513274595 + 1.7 = 3.213274595
y = 3.213274595

Simplifying
y = 3.213274595

Subproblem 2
y + -1.7 = -1.513274595

Simplifying
y + -1.7 = -1.513274595

Reorder the terms:
-1.7 + y = -1.513274595

Solving
-1.7 + y = -1.513274595

Solving for variable 'y'.

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

Add '1.7' to each side of the equation.
-1.7 + 1.7 + y = -1.513274595 + 1.7

Combine like terms: -1.7 + 1.7 = 0.0
0.0 + y = -1.513274595 + 1.7
y = -1.513274595 + 1.7

Combine like terms: -1.513274595 + 1.7 = 0.186725405
y = 0.186725405

Simplifying
y = 0.186725405

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.213274595, 0.186725405}