-4y(y+8)-5=51

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Solution for -4y(y+8)-5=51 equation: 


Simplifying
-4y(y + 8) + -5 = 51

Reorder the terms:
-4y(8 + y) + -5 = 51
(8 * -4y + y * -4y) + -5 = 51
(-32y + -4y2) + -5 = 51

Reorder the terms:
-5 + -32y + -4y2 = 51

Solving
-5 + -32y + -4y2 = 51

Solving for variable 'y'.

Reorder the terms:
-5 + -51 + -32y + -4y2 = 51 + -51

Combine like terms: -5 + -51 = -56
-56 + -32y + -4y2 = 51 + -51

Combine like terms: 51 + -51 = 0
-56 + -32y + -4y2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(14 + 8y + y2) = 0

Ignore the factor -4.

Subproblem 1
Set the factor '(14 + 8y + y2)' equal to zero and attempt to solve:

Simplifying
14 + 8y + y2 = 0

Solving
14 + 8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 8y + -14 + y2 = 0 + -14

Reorder the terms:
14 + -14 + 8y + y2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 8y + y2 = 0 + -14
8y + y2 = 0 + -14

Combine like terms: 0 + -14 = -14
8y + y2 = -14

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = -14 + 16

Reorder the terms:
16 + 8y + y2 = -14 + 16

Combine like terms: -14 + 16 = 2
16 + 8y + y2 = 2

Factor a perfect square on the left side:
(y + 4)(y + 4) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(y + 4) equal to 1.414213562 and -1.414213562.


Subproblem 1
y + 4 = 1.414213562

Simplifying
y + 4 = 1.414213562

Reorder the terms:
4 + y = 1.414213562

Solving
4 + y = 1.414213562

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = 1.414213562 + -4

Combine like terms: 4 + -4 = 0
0 + y = 1.414213562 + -4
y = 1.414213562 + -4

Combine like terms: 1.414213562 + -4 = -2.585786438
y = -2.585786438

Simplifying
y = -2.585786438


Subproblem 2
y + 4 = -1.414213562

Simplifying
y + 4 = -1.414213562

Reorder the terms:
4 + y = -1.414213562

Solving
4 + y = -1.414213562

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = -1.414213562 + -4

Combine like terms: 4 + -4 = 0
0 + y = -1.414213562 + -4
y = -1.414213562 + -4

Combine like terms: -1.414213562 + -4 = -5.414213562
y = -5.414213562

Simplifying
y = -5.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-2.585786438, -5.414213562}
Solution
y = {-2.585786438, -5.414213562}

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