2(4-y)7y=-1

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Solution for 2(4-y)7y=-1 equation: 


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

Reorder the terms for easier multiplication:
2 * 7y(4 + -1y) = -1

Multiply 2 * 7
14y(4 + -1y) = -1
(4 * 14y + -1y * 14y) = -1
(56y + -14y2) = -1

Solving
56y + -14y2 = -1

Solving for variable 'y'.

Reorder the terms:
1 + 56y + -14y2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 56y + -14y2 = 0

Begin completing the square.  Divide all terms by
-14 the coefficient of the squared term: 

Divide each side by '-14'.
-0.07142857143 + -4y + y2 = 0

Move the constant term to the right:

Add '0.07142857143' to each side of the equation.
-0.07142857143 + -4y + 0.07142857143 + y2 = 0 + 0.07142857143

Reorder the terms:
-0.07142857143 + 0.07142857143 + -4y + y2 = 0 + 0.07142857143

Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000
0.00000000000 + -4y + y2 = 0 + 0.07142857143
-4y + y2 = 0 + 0.07142857143

Combine like terms: 0 + 0.07142857143 = 0.07142857143
-4y + y2 = 0.07142857143

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 0.07142857143 + 4

Reorder the terms:
4 + -4y + y2 = 0.07142857143 + 4

Combine like terms: 0.07142857143 + 4 = 4.07142857143
4 + -4y + y2 = 4.07142857143

Factor a perfect square on the left side:
(y + -2)(y + -2) = 4.07142857143

Calculate the square root of the right side: 2.017778127

Break this problem into two subproblems by setting 
(y + -2) equal to 2.017778127 and -2.017778127.


Subproblem 1
y + -2 = 2.017778127

Simplifying
y + -2 = 2.017778127

Reorder the terms:
-2 + y = 2.017778127

Solving
-2 + y = 2.017778127

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 2.017778127 + 2

Combine like terms: -2 + 2 = 0
0 + y = 2.017778127 + 2
y = 2.017778127 + 2

Combine like terms: 2.017778127 + 2 = 4.017778127
y = 4.017778127

Simplifying
y = 4.017778127


Subproblem 2
y + -2 = -2.017778127

Simplifying
y + -2 = -2.017778127

Reorder the terms:
-2 + y = -2.017778127

Solving
-2 + y = -2.017778127

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -2.017778127 + 2

Combine like terms: -2 + 2 = 0
0 + y = -2.017778127 + 2
y = -2.017778127 + 2

Combine like terms: -2.017778127 + 2 = -0.017778127
y = -0.017778127

Simplifying
y = -0.017778127


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.017778127, -0.017778127}

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