16y(y+2)=2(7y+8)

Solution for 16y(y+2)=2(7y+8) equation:

Simplifying
16y(y + 2) = 2(7y + 8)

Reorder the terms:
16y(2 + y) = 2(7y + 8)
(2 * 16y + y * 16y) = 2(7y + 8)
(32y + 16y2) = 2(7y + 8)

Reorder the terms:
32y + 16y2 = 2(8 + 7y)
32y + 16y2 = (8 * 2 + 7y * 2)
32y + 16y2 = (16 + 14y)

Solving
32y + 16y2 = 16 + 14y

Solving for variable 'y'.

Reorder the terms:
-16 + 32y + -14y + 16y2 = 16 + 14y + -16 + -14y

Combine like terms: 32y + -14y = 18y
-16 + 18y + 16y2 = 16 + 14y + -16 + -14y

Reorder the terms:
-16 + 18y + 16y2 = 16 + -16 + 14y + -14y

Combine like terms: 16 + -16 = 0
-16 + 18y + 16y2 = 0 + 14y + -14y
-16 + 18y + 16y2 = 14y + -14y

Combine like terms: 14y + -14y = 0
-16 + 18y + 16y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 9y + 8y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + 9y + 8y2)' equal to zero and attempt to solve:

Simplifying
-8 + 9y + 8y2 = 0

Solving
-8 + 9y + 8y2 = 0

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

Divide each side by '8'.
-1 + 1.125y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.125y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.125y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.125y + y2 = 0 + 1
1.125y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.125y + y2 = 1

The y term is 1.125y.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125y + 0.31640625 + y2 = 1 + 0.31640625

Reorder the terms:
0.31640625 + 1.125y + y2 = 1 + 0.31640625

Combine like terms: 1 + 0.31640625 = 1.31640625
0.31640625 + 1.125y + y2 = 1.31640625

Factor a perfect square on the left side:
(y + 0.5625)(y + 0.5625) = 1.31640625

Calculate the square root of the right side: 1.147347484

Break this problem into two subproblems by setting 
(y + 0.5625) equal to 1.147347484 and -1.147347484.

Subproblem 1
y + 0.5625 = 1.147347484

Simplifying
y + 0.5625 = 1.147347484

Reorder the terms:
0.5625 + y = 1.147347484

Solving
0.5625 + y = 1.147347484

Solving for variable 'y'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + y = 1.147347484 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + y = 1.147347484 + -0.5625
y = 1.147347484 + -0.5625

Combine like terms: 1.147347484 + -0.5625 = 0.584847484
y = 0.584847484

Simplifying
y = 0.584847484

Subproblem 2
y + 0.5625 = -1.147347484

Simplifying
y + 0.5625 = -1.147347484

Reorder the terms:
0.5625 + y = -1.147347484

Solving
0.5625 + y = -1.147347484

Solving for variable 'y'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + y = -1.147347484 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + y = -1.147347484 + -0.5625
y = -1.147347484 + -0.5625

Combine like terms: -1.147347484 + -0.5625 = -1.709847484
y = -1.709847484

Simplifying
y = -1.709847484

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.584847484, -1.709847484}
Solution
y = {0.584847484, -1.709847484}