0=3y^2+23y+38

Solution for 0=3y^2+23y+38 equation:

Simplifying
0 = 3y2 + 23y + 38

Reorder the terms:
0 = 38 + 23y + 3y2

Solving
0 = 38 + 23y + 3y2

Solving for variable 'y'.

Combine like terms: 0 + -38 = -38
-38 + -23y + -3y2 = 38 + 23y + 3y2 + -38 + -23y + -3y2

Reorder the terms:
-38 + -23y + -3y2 = 38 + -38 + 23y + -23y + 3y2 + -3y2

Combine like terms: 38 + -38 = 0
-38 + -23y + -3y2 = 0 + 23y + -23y + 3y2 + -3y2
-38 + -23y + -3y2 = 23y + -23y + 3y2 + -3y2

Combine like terms: 23y + -23y = 0
-38 + -23y + -3y2 = 0 + 3y2 + -3y2
-38 + -23y + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-38 + -23y + -3y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(38 + 23y + 3y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(38 + 23y + 3y2)' equal to zero and attempt to solve:

Simplifying
38 + 23y + 3y2 = 0

Solving
38 + 23y + 3y2 = 0

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

Divide each side by '3'.
12.66666667 + 7.666666667y + y2 = 0

Move the constant term to the right:

Add '-12.66666667' to each side of the equation.
12.66666667 + 7.666666667y + -12.66666667 + y2 = 0 + -12.66666667

Reorder the terms:
12.66666667 + -12.66666667 + 7.666666667y + y2 = 0 + -12.66666667

Combine like terms: 12.66666667 + -12.66666667 = 0.00000000
0.00000000 + 7.666666667y + y2 = 0 + -12.66666667
7.666666667y + y2 = 0 + -12.66666667

Combine like terms: 0 + -12.66666667 = -12.66666667
7.666666667y + y2 = -12.66666667

The y term is 7.666666667y.  Take half its coefficient (3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
7.666666667y + 14.69444445 + y2 = -12.66666667 + 14.69444445

Reorder the terms:
14.69444445 + 7.666666667y + y2 = -12.66666667 + 14.69444445

Combine like terms: -12.66666667 + 14.69444445 = 2.02777778
14.69444445 + 7.666666667y + y2 = 2.02777778

Factor a perfect square on the left side:
(y + 3.833333334)(y + 3.833333334) = 2.02777778

Calculate the square root of the right side: 1.424000625

Break this problem into two subproblems by setting 
(y + 3.833333334) equal to 1.424000625 and -1.424000625.

Subproblem 1
y + 3.833333334 = 1.424000625

Simplifying
y + 3.833333334 = 1.424000625

Reorder the terms:
3.833333334 + y = 1.424000625

Solving
3.833333334 + y = 1.424000625

Solving for variable 'y'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + y = 1.424000625 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + y = 1.424000625 + -3.833333334
y = 1.424000625 + -3.833333334

Combine like terms: 1.424000625 + -3.833333334 = -2.409332709
y = -2.409332709

Simplifying
y = -2.409332709

Subproblem 2
y + 3.833333334 = -1.424000625

Simplifying
y + 3.833333334 = -1.424000625

Reorder the terms:
3.833333334 + y = -1.424000625

Solving
3.833333334 + y = -1.424000625

Solving for variable 'y'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + y = -1.424000625 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + y = -1.424000625 + -3.833333334
y = -1.424000625 + -3.833333334

Combine like terms: -1.424000625 + -3.833333334 = -5.257333959
y = -5.257333959

Simplifying
y = -5.257333959

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-2.409332709, -5.257333959}
Solution
y = {-2.409332709, -5.257333959}