3y^2-16y+15=0

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Solution for 3y^2-16y+15=0 equation: 


Simplifying
3y2 + -16y + 15 = 0

Reorder the terms:
15 + -16y + 3y2 = 0

Solving
15 + -16y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
5 + -5.333333333y + y2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -5.333333333y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + -5.333333333y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -5.333333333y + y2 = 0 + -5
-5.333333333y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
-5.333333333y + y2 = -5

The y term is -5.333333333y.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333y + 7.111111113 + y2 = -5 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333y + y2 = -5 + 7.111111113

Combine like terms: -5 + 7.111111113 = 2.111111113
7.111111113 + -5.333333333y + y2 = 2.111111113

Factor a perfect square on the left side:
(y + -2.666666667)(y + -2.666666667) = 2.111111113

Calculate the square root of the right side: 1.452966315

Break this problem into two subproblems by setting 
(y + -2.666666667) equal to 1.452966315 and -1.452966315.


Subproblem 1
y + -2.666666667 = 1.452966315

Simplifying
y + -2.666666667 = 1.452966315

Reorder the terms:
-2.666666667 + y = 1.452966315

Solving
-2.666666667 + y = 1.452966315

Solving for variable 'y'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + y = 1.452966315 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + y = 1.452966315 + 2.666666667
y = 1.452966315 + 2.666666667

Combine like terms: 1.452966315 + 2.666666667 = 4.119632982
y = 4.119632982

Simplifying
y = 4.119632982


Subproblem 2
y + -2.666666667 = -1.452966315

Simplifying
y + -2.666666667 = -1.452966315

Reorder the terms:
-2.666666667 + y = -1.452966315

Solving
-2.666666667 + y = -1.452966315

Solving for variable 'y'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + y = -1.452966315 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + y = -1.452966315 + 2.666666667
y = -1.452966315 + 2.666666667

Combine like terms: -1.452966315 + 2.666666667 = 1.213700352
y = 1.213700352

Simplifying
y = 1.213700352


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.119632982, 1.213700352}

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