3y^2-29y+12=0

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Solution for 3y^2-29y+12=0 equation: 


Simplifying
3y2 + -29y + 12 = 0

Reorder the terms:
12 + -29y + 3y2 = 0

Solving
12 + -29y + 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'.
4 + -9.666666667y + y2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -9.666666667y + -4 + y2 = 0 + -4

Reorder the terms:
4 + -4 + -9.666666667y + y2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9.666666667y + y2 = 0 + -4
-9.666666667y + y2 = 0 + -4

Combine like terms: 0 + -4 = -4
-9.666666667y + y2 = -4

The y term is -9.666666667y.  Take half its coefficient (-4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
-9.666666667y + 23.36111112 + y2 = -4 + 23.36111112

Reorder the terms:
23.36111112 + -9.666666667y + y2 = -4 + 23.36111112

Combine like terms: -4 + 23.36111112 = 19.36111112
23.36111112 + -9.666666667y + y2 = 19.36111112

Factor a perfect square on the left side:
(y + -4.833333334)(y + -4.833333334) = 19.36111112

Calculate the square root of the right side: 4.400126262

Break this problem into two subproblems by setting 
(y + -4.833333334) equal to 4.400126262 and -4.400126262.


Subproblem 1
y + -4.833333334 = 4.400126262

Simplifying
y + -4.833333334 = 4.400126262

Reorder the terms:
-4.833333334 + y = 4.400126262

Solving
-4.833333334 + y = 4.400126262

Solving for variable 'y'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + y = 4.400126262 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + y = 4.400126262 + 4.833333334
y = 4.400126262 + 4.833333334

Combine like terms: 4.400126262 + 4.833333334 = 9.233459596
y = 9.233459596

Simplifying
y = 9.233459596


Subproblem 2
y + -4.833333334 = -4.400126262

Simplifying
y + -4.833333334 = -4.400126262

Reorder the terms:
-4.833333334 + y = -4.400126262

Solving
-4.833333334 + y = -4.400126262

Solving for variable 'y'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + y = -4.400126262 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + y = -4.400126262 + 4.833333334
y = -4.400126262 + 4.833333334

Combine like terms: -4.400126262 + 4.833333334 = 0.433207072
y = 0.433207072

Simplifying
y = 0.433207072


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.233459596, 0.433207072}

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