2y+2y(y-2)=6y-4(y-10)

Solution for 2y+2y(y-2)=6y-4(y-10) equation:

Simplifying
2y + 2y(y + -2) = 6y + -4(y + -10)

Reorder the terms:
2y + 2y(-2 + y) = 6y + -4(y + -10)
2y + (-2 * 2y + y * 2y) = 6y + -4(y + -10)
2y + (-4y + 2y2) = 6y + -4(y + -10)

Combine like terms: 2y + -4y = -2y
-2y + 2y2 = 6y + -4(y + -10)

Reorder the terms:
-2y + 2y2 = 6y + -4(-10 + y)
-2y + 2y2 = 6y + (-10 * -4 + y * -4)
-2y + 2y2 = 6y + (40 + -4y)

Reorder the terms:
-2y + 2y2 = 40 + 6y + -4y

Combine like terms: 6y + -4y = 2y
-2y + 2y2 = 40 + 2y

Solving
-2y + 2y2 = 40 + 2y

Solving for variable 'y'.

Reorder the terms:
-40 + -2y + -2y + 2y2 = 40 + 2y + -40 + -2y

Combine like terms: -2y + -2y = -4y
-40 + -4y + 2y2 = 40 + 2y + -40 + -2y

Reorder the terms:
-40 + -4y + 2y2 = 40 + -40 + 2y + -2y

Combine like terms: 40 + -40 = 0
-40 + -4y + 2y2 = 0 + 2y + -2y
-40 + -4y + 2y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-40 + -4y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -2y + y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-20 + -2y + y2)' equal to zero and attempt to solve:

Simplifying
-20 + -2y + y2 = 0

Solving
-20 + -2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -2y + 20 + y2 = 0 + 20

Reorder the terms:
-20 + 20 + -2y + y2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -2y + y2 = 0 + 20
-2y + y2 = 0 + 20

Combine like terms: 0 + 20 = 20
-2y + y2 = 20

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 20 + 1

Reorder the terms:
1 + -2y + y2 = 20 + 1

Combine like terms: 20 + 1 = 21
1 + -2y + y2 = 21

Factor a perfect square on the left side:
(y + -1)(y + -1) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(y + -1) equal to 4.582575695 and -4.582575695.

Subproblem 1
y + -1 = 4.582575695

Simplifying
y + -1 = 4.582575695

Reorder the terms:
-1 + y = 4.582575695

Solving
-1 + y = 4.582575695

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 4.582575695 + 1

Combine like terms: -1 + 1 = 0
0 + y = 4.582575695 + 1
y = 4.582575695 + 1

Combine like terms: 4.582575695 + 1 = 5.582575695
y = 5.582575695

Simplifying
y = 5.582575695

Subproblem 2
y + -1 = -4.582575695

Simplifying
y + -1 = -4.582575695

Reorder the terms:
-1 + y = -4.582575695

Solving
-1 + y = -4.582575695

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -4.582575695 + 1

Combine like terms: -1 + 1 = 0
0 + y = -4.582575695 + 1
y = -4.582575695 + 1

Combine like terms: -4.582575695 + 1 = -3.582575695
y = -3.582575695

Simplifying
y = -3.582575695

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.582575695, -3.582575695}
Solution
y = {5.582575695, -3.582575695}