-2y(7-y)+4=-4

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Solution for -2y(7-y)+4=-4 equation: 


Simplifying
-2y(7 + -1y) + 4 = -4
(7 * -2y + -1y * -2y) + 4 = -4
(-14y + 2y2) + 4 = -4

Reorder the terms:
4 + -14y + 2y2 = -4

Solving
4 + -14y + 2y2 = -4

Solving for variable 'y'.

Reorder the terms:
4 + 4 + -14y + 2y2 = -4 + 4

Combine like terms: 4 + 4 = 8
8 + -14y + 2y2 = -4 + 4

Combine like terms: -4 + 4 = 0
8 + -14y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -7y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -7y + y2)' equal to zero and attempt to solve:

Simplifying
4 + -7y + y2 = 0

Solving
4 + -7y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -7y + -4 + y2 = 0 + -4

Reorder the terms:
4 + -4 + -7y + y2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7y + y2 = 0 + -4
-7y + y2 = 0 + -4

Combine like terms: 0 + -4 = -4
-7y + y2 = -4

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = -4 + 12.25

Reorder the terms:
12.25 + -7y + y2 = -4 + 12.25

Combine like terms: -4 + 12.25 = 8.25
12.25 + -7y + y2 = 8.25

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(y + -3.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
y + -3.5 = 2.872281323

Simplifying
y + -3.5 = 2.872281323

Reorder the terms:
-3.5 + y = 2.872281323

Solving
-3.5 + y = 2.872281323

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = 2.872281323 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = 2.872281323 + 3.5
y = 2.872281323 + 3.5

Combine like terms: 2.872281323 + 3.5 = 6.372281323
y = 6.372281323

Simplifying
y = 6.372281323


Subproblem 2
y + -3.5 = -2.872281323

Simplifying
y + -3.5 = -2.872281323

Reorder the terms:
-3.5 + y = -2.872281323

Solving
-3.5 + y = -2.872281323

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = -2.872281323 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = -2.872281323 + 3.5
y = -2.872281323 + 3.5

Combine like terms: -2.872281323 + 3.5 = 0.627718677
y = 0.627718677

Simplifying
y = 0.627718677


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.372281323, 0.627718677}
Solution
y = {6.372281323, 0.627718677}

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