-2(4y+4)8y=-16

Solution for -2(4y+4)8y=-16 equation:

Simplifying
-2(4y + 4) * 8y = -16

Reorder the terms:
-2(4 + 4y) * 8y = -16

Reorder the terms for easier multiplication:
-2 * 8y(4 + 4y) = -16

Multiply -2 * 8
-16y(4 + 4y) = -16
(4 * -16y + 4y * -16y) = -16
(-64y + -64y2) = -16

Solving
-64y + -64y2 = -16

Solving for variable 'y'.

Reorder the terms:
16 + -64y + -64y2 = -16 + 16

Combine like terms: -16 + 16 = 0
16 + -64y + -64y2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(1 + -4y + -4y2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(1 + -4y + -4y2)' equal to zero and attempt to solve:

Simplifying
1 + -4y + -4y2 = 0

Solving
1 + -4y + -4y2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + y + y2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + y + 0.25 + y2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + y + y2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y + y2 = 0 + 0.25
y + y2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
y + y2 = 0.25

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + y2 = 0.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + y2 = 0.25 + 0.25

Combine like terms: 0.25 + 0.25 = 0.5
1.25 + y2 = 0.5

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(y + 0.5) equal to 0.707106781 and -0.707106781.

Subproblem 1
y + 0.5 = 0.707106781

Simplifying
y + 0.5 = 0.707106781

Reorder the terms:
0.5 + y = 0.707106781

Solving
0.5 + y = 0.707106781

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 0.707106781 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 0.707106781 + -0.5
y = 0.707106781 + -0.5

Combine like terms: 0.707106781 + -0.5 = 0.207106781
y = 0.207106781

Simplifying
y = 0.207106781

Subproblem 2
y + 0.5 = -0.707106781

Simplifying
y + 0.5 = -0.707106781

Reorder the terms:
0.5 + y = -0.707106781

Solving
0.5 + y = -0.707106781

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -0.707106781 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -0.707106781 + -0.5
y = -0.707106781 + -0.5

Combine like terms: -0.707106781 + -0.5 = -1.207106781
y = -1.207106781

Simplifying
y = -1.207106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.207106781, -1.207106781}
Solution
y = {0.207106781, -1.207106781}