-26+26y=2y(-4y-2)

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Solution for -26+26y=2y(-4y-2) equation: 


Simplifying
-26 + 26y = 2y(-4y + -2)

Reorder the terms:
-26 + 26y = 2y(-2 + -4y)
-26 + 26y = (-2 * 2y + -4y * 2y)
-26 + 26y = (-4y + -8y2)

Solving
-26 + 26y = -4y + -8y2

Solving for variable 'y'.

Combine like terms: 26y + 4y = 30y
-26 + 30y + 8y2 = -4y + -8y2 + 4y + 8y2

Reorder the terms:
-26 + 30y + 8y2 = -4y + 4y + -8y2 + 8y2

Combine like terms: -4y + 4y = 0
-26 + 30y + 8y2 = 0 + -8y2 + 8y2
-26 + 30y + 8y2 = -8y2 + 8y2

Combine like terms: -8y2 + 8y2 = 0
-26 + 30y + 8y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 15y + 4y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-13 + 15y + 4y2)' equal to zero and attempt to solve:

Simplifying
-13 + 15y + 4y2 = 0

Solving
-13 + 15y + 4y2 = 0

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

Divide each side by '4'.
-3.25 + 3.75y + y2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + 3.75y + 3.25 + y2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + 3.75y + y2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + 3.75y + y2 = 0 + 3.25
3.75y + y2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
3.75y + y2 = 3.25

The y term is 3.75y.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75y + 3.515625 + y2 = 3.25 + 3.515625

Reorder the terms:
3.515625 + 3.75y + y2 = 3.25 + 3.515625

Combine like terms: 3.25 + 3.515625 = 6.765625
3.515625 + 3.75y + y2 = 6.765625

Factor a perfect square on the left side:
(y + 1.875)(y + 1.875) = 6.765625

Calculate the square root of the right side: 2.601081506

Break this problem into two subproblems by setting 
(y + 1.875) equal to 2.601081506 and -2.601081506.


Subproblem 1
y + 1.875 = 2.601081506

Simplifying
y + 1.875 = 2.601081506

Reorder the terms:
1.875 + y = 2.601081506

Solving
1.875 + y = 2.601081506

Solving for variable 'y'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + y = 2.601081506 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + y = 2.601081506 + -1.875
y = 2.601081506 + -1.875

Combine like terms: 2.601081506 + -1.875 = 0.726081506
y = 0.726081506

Simplifying
y = 0.726081506


Subproblem 2
y + 1.875 = -2.601081506

Simplifying
y + 1.875 = -2.601081506

Reorder the terms:
1.875 + y = -2.601081506

Solving
1.875 + y = -2.601081506

Solving for variable 'y'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + y = -2.601081506 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + y = -2.601081506 + -1.875
y = -2.601081506 + -1.875

Combine like terms: -2.601081506 + -1.875 = -4.476081506
y = -4.476081506

Simplifying
y = -4.476081506


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.726081506, -4.476081506}
Solution
y = {0.726081506, -4.476081506}

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