3y^2-39y+6=0

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Solution for 3y^2-39y+6=0 equation: 


Simplifying
3y2 + -39y + 6 = 0

Reorder the terms:
6 + -39y + 3y2 = 0

Solving
6 + -39y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -13y + y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -13y + y2)' equal to zero and attempt to solve:

Simplifying
2 + -13y + y2 = 0

Solving
2 + -13y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -13y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + -13y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -13y + y2 = 0 + -2
-13y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-13y + y2 = -2

The y term is -13y.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13y + 42.25 + y2 = -2 + 42.25

Reorder the terms:
42.25 + -13y + y2 = -2 + 42.25

Combine like terms: -2 + 42.25 = 40.25
42.25 + -13y + y2 = 40.25

Factor a perfect square on the left side:
(y + -6.5)(y + -6.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(y + -6.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
y + -6.5 = 6.34428877

Simplifying
y + -6.5 = 6.34428877

Reorder the terms:
-6.5 + y = 6.34428877

Solving
-6.5 + y = 6.34428877

Solving for variable 'y'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + y = 6.34428877 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + y = 6.34428877 + 6.5
y = 6.34428877 + 6.5

Combine like terms: 6.34428877 + 6.5 = 12.84428877
y = 12.84428877

Simplifying
y = 12.84428877


Subproblem 2
y + -6.5 = -6.34428877

Simplifying
y + -6.5 = -6.34428877

Reorder the terms:
-6.5 + y = -6.34428877

Solving
-6.5 + y = -6.34428877

Solving for variable 'y'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + y = -6.34428877 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + y = -6.34428877 + 6.5
y = -6.34428877 + 6.5

Combine like terms: -6.34428877 + 6.5 = 0.15571123
y = 0.15571123

Simplifying
y = 0.15571123


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {12.84428877, 0.15571123}
Solution
y = {12.84428877, 0.15571123}

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