6y^2-8y+12-12y^2-8y+7=

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Solution for 6y^2-8y+12-12y^2-8y+7= equation: 


Simplifying
6y2 + -8y + 12 + -12y2 + -8y + 7 = 0

Reorder the terms:
12 + 7 + -8y + -8y + 6y2 + -12y2 = 0

Combine like terms: 12 + 7 = 19
19 + -8y + -8y + 6y2 + -12y2 = 0

Combine like terms: -8y + -8y = -16y
19 + -16y + 6y2 + -12y2 = 0

Combine like terms: 6y2 + -12y2 = -6y2
19 + -16y + -6y2 = 0

Solving
19 + -16y + -6y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-3.166666667 + 2.666666667y + y2 = 0

Move the constant term to the right:

Add '3.166666667' to each side of the equation.
-3.166666667 + 2.666666667y + 3.166666667 + y2 = 0 + 3.166666667

Reorder the terms:
-3.166666667 + 3.166666667 + 2.666666667y + y2 = 0 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + 2.666666667y + y2 = 0 + 3.166666667
2.666666667y + y2 = 0 + 3.166666667

Combine like terms: 0 + 3.166666667 = 3.166666667
2.666666667y + y2 = 3.166666667

The y term is 2.666666667y.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667y + 1.777777780 + y2 = 3.166666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667y + y2 = 3.166666667 + 1.777777780

Combine like terms: 3.166666667 + 1.777777780 = 4.944444447
1.777777780 + 2.666666667y + y2 = 4.944444447

Factor a perfect square on the left side:
(y + 1.333333334)(y + 1.333333334) = 4.944444447

Calculate the square root of the right side: 2.223610678

Break this problem into two subproblems by setting 
(y + 1.333333334) equal to 2.223610678 and -2.223610678.


Subproblem 1
y + 1.333333334 = 2.223610678

Simplifying
y + 1.333333334 = 2.223610678

Reorder the terms:
1.333333334 + y = 2.223610678

Solving
1.333333334 + y = 2.223610678

Solving for variable 'y'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + y = 2.223610678 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + y = 2.223610678 + -1.333333334
y = 2.223610678 + -1.333333334

Combine like terms: 2.223610678 + -1.333333334 = 0.890277344
y = 0.890277344

Simplifying
y = 0.890277344


Subproblem 2
y + 1.333333334 = -2.223610678

Simplifying
y + 1.333333334 = -2.223610678

Reorder the terms:
1.333333334 + y = -2.223610678

Solving
1.333333334 + y = -2.223610678

Solving for variable 'y'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + y = -2.223610678 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + y = -2.223610678 + -1.333333334
y = -2.223610678 + -1.333333334

Combine like terms: -2.223610678 + -1.333333334 = -3.556944012
y = -3.556944012

Simplifying
y = -3.556944012


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.890277344, -3.556944012}

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