4y^2+16y+8=14

Solution for 4y^2+16y+8=14 equation:

Simplifying
4y2 + 16y + 8 = 14

Reorder the terms:
8 + 16y + 4y2 = 14

Solving
8 + 16y + 4y2 = 14

Solving for variable 'y'.

Reorder the terms:
8 + -14 + 16y + 4y2 = 14 + -14

Combine like terms: 8 + -14 = -6
-6 + 16y + 4y2 = 14 + -14

Combine like terms: 14 + -14 = 0
-6 + 16y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 8y + 2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 8y + 2y2)' equal to zero and attempt to solve:

Simplifying
-3 + 8y + 2y2 = 0

Solving
-3 + 8y + 2y2 = 0

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

Divide each side by '2'.
-1.5 + 4y + y2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 4y + 1.5 + y2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 4y + y2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 4y + y2 = 0 + 1.5
4y + y2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
4y + y2 = 1.5

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 = 1.5 + 4

Reorder the terms:
4 + 4y + y2 = 1.5 + 4

Combine like terms: 1.5 + 4 = 5.5
4 + 4y + y2 = 5.5

Factor a perfect square on the left side:
(y + 2)(y + 2) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(y + 2) equal to 2.34520788 and -2.34520788.

Subproblem 1
y + 2 = 2.34520788

Simplifying
y + 2 = 2.34520788

Reorder the terms:
2 + y = 2.34520788

Solving
2 + y = 2.34520788

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 = 2.34520788 + -2

Combine like terms: 2 + -2 = 0
0 + y = 2.34520788 + -2
y = 2.34520788 + -2

Combine like terms: 2.34520788 + -2 = 0.34520788
y = 0.34520788

Simplifying
y = 0.34520788

Subproblem 2
y + 2 = -2.34520788

Simplifying
y + 2 = -2.34520788

Reorder the terms:
2 + y = -2.34520788

Solving
2 + y = -2.34520788

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 = -2.34520788 + -2

Combine like terms: 2 + -2 = 0
0 + y = -2.34520788 + -2
y = -2.34520788 + -2

Combine like terms: -2.34520788 + -2 = -4.34520788
y = -4.34520788

Simplifying
y = -4.34520788

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.34520788, -4.34520788}
Solution
y = {0.34520788, -4.34520788}