4y^2-2y-8=0

Solution for 4y^2-2y-8=0 equation:

Simplifying
4y2 + -2y + -8 = 0

Reorder the terms:
-8 + -2y + 4y2 = 0

Solving
-8 + -2y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -1y + 2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1y + 2y2)' equal to zero and attempt to solve:

Simplifying
-4 + -1y + 2y2 = 0

Solving
-4 + -1y + 2y2 = 0

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

Divide each side by '2'.
-2 + -0.5y + y2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.5y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.5y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.5y + y2 = 0 + 2
-0.5y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.5y + y2 = 2

The y term is -0.5y.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5y + 0.0625 + y2 = 2 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = 2 + 0.0625

Combine like terms: 2 + 0.0625 = 2.0625
0.0625 + -0.5y + y2 = 2.0625

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(y + -0.25) equal to 1.436140662 and -1.436140662.

Subproblem 1
y + -0.25 = 1.436140662

Simplifying
y + -0.25 = 1.436140662

Reorder the terms:
-0.25 + y = 1.436140662

Solving
-0.25 + y = 1.436140662

Solving for variable 'y'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + y = 1.436140662 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = 1.436140662 + 0.25
y = 1.436140662 + 0.25

Combine like terms: 1.436140662 + 0.25 = 1.686140662
y = 1.686140662

Simplifying
y = 1.686140662

Subproblem 2
y + -0.25 = -1.436140662

Simplifying
y + -0.25 = -1.436140662

Reorder the terms:
-0.25 + y = -1.436140662

Solving
-0.25 + y = -1.436140662

Solving for variable 'y'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + y = -1.436140662 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = -1.436140662 + 0.25
y = -1.436140662 + 0.25

Combine like terms: -1.436140662 + 0.25 = -1.186140662
y = -1.186140662

Simplifying
y = -1.186140662

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.686140662, -1.186140662}
Solution
y = {1.686140662, -1.186140662}