14y^2-80y-66=0

Solution for 14y^2-80y-66=0 equation:

Simplifying
14y2 + -80y + -66 = 0

Reorder the terms:
-66 + -80y + 14y2 = 0

Solving
-66 + -80y + 14y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + -40y + 7y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-33 + -40y + 7y2)' equal to zero and attempt to solve:

Simplifying
-33 + -40y + 7y2 = 0

Solving
-33 + -40y + 7y2 = 0

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

Divide each side by '7'.
-4.714285714 + -5.714285714y + y2 = 0

Move the constant term to the right:

Add '4.714285714' to each side of the equation.
-4.714285714 + -5.714285714y + 4.714285714 + y2 = 0 + 4.714285714

Reorder the terms:
-4.714285714 + 4.714285714 + -5.714285714y + y2 = 0 + 4.714285714

Combine like terms: -4.714285714 + 4.714285714 = 0.000000000
0.000000000 + -5.714285714y + y2 = 0 + 4.714285714
-5.714285714y + y2 = 0 + 4.714285714

Combine like terms: 0 + 4.714285714 = 4.714285714
-5.714285714y + y2 = 4.714285714

The y term is -5.714285714y.  Take half its coefficient (-2.857142857).
Square it (8.163265305) and add it to both sides.

Add '8.163265305' to each side of the equation.
-5.714285714y + 8.163265305 + y2 = 4.714285714 + 8.163265305

Reorder the terms:
8.163265305 + -5.714285714y + y2 = 4.714285714 + 8.163265305

Combine like terms: 4.714285714 + 8.163265305 = 12.877551019
8.163265305 + -5.714285714y + y2 = 12.877551019

Factor a perfect square on the left side:
(y + -2.857142857)(y + -2.857142857) = 12.877551019

Calculate the square root of the right side: 3.588530482

Break this problem into two subproblems by setting 
(y + -2.857142857) equal to 3.588530482 and -3.588530482.

Subproblem 1
y + -2.857142857 = 3.588530482

Simplifying
y + -2.857142857 = 3.588530482

Reorder the terms:
-2.857142857 + y = 3.588530482

Solving
-2.857142857 + y = 3.588530482

Solving for variable 'y'.

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

Add '2.857142857' to each side of the equation.
-2.857142857 + 2.857142857 + y = 3.588530482 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + y = 3.588530482 + 2.857142857
y = 3.588530482 + 2.857142857

Combine like terms: 3.588530482 + 2.857142857 = 6.445673339
y = 6.445673339

Simplifying
y = 6.445673339

Subproblem 2
y + -2.857142857 = -3.588530482

Simplifying
y + -2.857142857 = -3.588530482

Reorder the terms:
-2.857142857 + y = -3.588530482

Solving
-2.857142857 + y = -3.588530482

Solving for variable 'y'.

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

Add '2.857142857' to each side of the equation.
-2.857142857 + 2.857142857 + y = -3.588530482 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + y = -3.588530482 + 2.857142857
y = -3.588530482 + 2.857142857

Combine like terms: -3.588530482 + 2.857142857 = -0.731387625
y = -0.731387625

Simplifying
y = -0.731387625

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.445673339, -0.731387625}
Solution
y = {6.445673339, -0.731387625}