2y(y+16)=14

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Solution for 2y(y+16)=14 equation:


Simplifying
2y(y + 16) = 14

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

Solving
32y + 2y2 = 14

Solving for variable 'y'.

Reorder the terms:
-14 + 32y + 2y2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 32y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 16y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 16y + y2)' equal to zero and attempt to solve:

Simplifying
-7 + 16y + y2 = 0

Solving
-7 + 16y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 16y + 7 + y2 = 0 + 7

Reorder the terms:
-7 + 7 + 16y + y2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 16y + y2 = 0 + 7
16y + y2 = 0 + 7

Combine like terms: 0 + 7 = 7
16y + y2 = 7

The y term is 16y.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16y + 64 + y2 = 7 + 64

Reorder the terms:
64 + 16y + y2 = 7 + 64

Combine like terms: 7 + 64 = 71
64 + 16y + y2 = 71

Factor a perfect square on the left side:
(y + 8)(y + 8) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(y + 8) equal to 8.426149773 and -8.426149773.


Subproblem 1
y + 8 = 8.426149773

Simplifying
y + 8 = 8.426149773

Reorder the terms:
8 + y = 8.426149773

Solving
8 + y = 8.426149773

Solving for variable 'y'.

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

Add '-8' to each side of the equation.
8 + -8 + y = 8.426149773 + -8

Combine like terms: 8 + -8 = 0
0 + y = 8.426149773 + -8
y = 8.426149773 + -8

Combine like terms: 8.426149773 + -8 = 0.426149773
y = 0.426149773

Simplifying
y = 0.426149773


Subproblem 2
y + 8 = -8.426149773

Simplifying
y + 8 = -8.426149773

Reorder the terms:
8 + y = -8.426149773

Solving
8 + y = -8.426149773

Solving for variable 'y'.

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

Add '-8' to each side of the equation.
8 + -8 + y = -8.426149773 + -8

Combine like terms: 8 + -8 = 0
0 + y = -8.426149773 + -8
y = -8.426149773 + -8

Combine like terms: -8.426149773 + -8 = -16.426149773
y = -16.426149773

Simplifying
y = -16.426149773


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.426149773, -16.426149773}
Solution
y = {0.426149773, -16.426149773}

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