(2y+12)(2y+12)=96

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Solution for (2y+12)(2y+12)=96 equation: 


Simplifying
(2y + 12)(2y + 12) = 96

Reorder the terms:
(12 + 2y)(2y + 12) = 96

Reorder the terms:
(12 + 2y)(12 + 2y) = 96

Multiply (12 + 2y) * (12 + 2y)
(12(12 + 2y) + 2y * (12 + 2y)) = 96
((12 * 12 + 2y * 12) + 2y * (12 + 2y)) = 96
((144 + 24y) + 2y * (12 + 2y)) = 96
(144 + 24y + (12 * 2y + 2y * 2y)) = 96
(144 + 24y + (24y + 4y2)) = 96

Combine like terms: 24y + 24y = 48y
(144 + 48y + 4y2) = 96

Solving
144 + 48y + 4y2 = 96

Solving for variable 'y'.

Reorder the terms:
144 + -96 + 48y + 4y2 = 96 + -96

Combine like terms: 144 + -96 = 48
48 + 48y + 4y2 = 96 + -96

Combine like terms: 96 + -96 = 0
48 + 48y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + 12y + y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(12 + 12y + y2)' equal to zero and attempt to solve:

Simplifying
12 + 12y + y2 = 0

Solving
12 + 12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 12y + -12 + y2 = 0 + -12

Reorder the terms:
12 + -12 + 12y + y2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 12y + y2 = 0 + -12
12y + y2 = 0 + -12

Combine like terms: 0 + -12 = -12
12y + y2 = -12

The y term is 12y.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12y + 36 + y2 = -12 + 36

Reorder the terms:
36 + 12y + y2 = -12 + 36

Combine like terms: -12 + 36 = 24
36 + 12y + y2 = 24

Factor a perfect square on the left side:
(y + 6)(y + 6) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(y + 6) equal to 4.898979486 and -4.898979486.


Subproblem 1
y + 6 = 4.898979486

Simplifying
y + 6 = 4.898979486

Reorder the terms:
6 + y = 4.898979486

Solving
6 + y = 4.898979486

Solving for variable 'y'.

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

Add '-6' to each side of the equation.
6 + -6 + y = 4.898979486 + -6

Combine like terms: 6 + -6 = 0
0 + y = 4.898979486 + -6
y = 4.898979486 + -6

Combine like terms: 4.898979486 + -6 = -1.101020514
y = -1.101020514

Simplifying
y = -1.101020514


Subproblem 2
y + 6 = -4.898979486

Simplifying
y + 6 = -4.898979486

Reorder the terms:
6 + y = -4.898979486

Solving
6 + y = -4.898979486

Solving for variable 'y'.

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

Add '-6' to each side of the equation.
6 + -6 + y = -4.898979486 + -6

Combine like terms: 6 + -6 = 0
0 + y = -4.898979486 + -6
y = -4.898979486 + -6

Combine like terms: -4.898979486 + -6 = -10.898979486
y = -10.898979486

Simplifying
y = -10.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-1.101020514, -10.898979486}
Solution
y = {-1.101020514, -10.898979486}

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