(8y-12)12y=68

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Solution for (8y-12)12y=68 equation: 


Simplifying
(8y + -12) * 12y = 68

Reorder the terms:
(-12 + 8y) * 12y = 68

Reorder the terms for easier multiplication:
12y(-12 + 8y) = 68
(-12 * 12y + 8y * 12y) = 68
(-144y + 96y2) = 68

Solving
-144y + 96y2 = 68

Solving for variable 'y'.

Reorder the terms:
-68 + -144y + 96y2 = 68 + -68

Combine like terms: 68 + -68 = 0
-68 + -144y + 96y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-17 + -36y + 24y2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-17 + -36y + 24y2)' equal to zero and attempt to solve:

Simplifying
-17 + -36y + 24y2 = 0

Solving
-17 + -36y + 24y2 = 0

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

Divide each side by '24'.
-0.7083333333 + -1.5y + y2 = 0

Move the constant term to the right:

Add '0.7083333333' to each side of the equation.
-0.7083333333 + -1.5y + 0.7083333333 + y2 = 0 + 0.7083333333

Reorder the terms:
-0.7083333333 + 0.7083333333 + -1.5y + y2 = 0 + 0.7083333333

Combine like terms: -0.7083333333 + 0.7083333333 = 0.0000000000
0.0000000000 + -1.5y + y2 = 0 + 0.7083333333
-1.5y + y2 = 0 + 0.7083333333

Combine like terms: 0 + 0.7083333333 = 0.7083333333
-1.5y + y2 = 0.7083333333

The y term is -1.5y.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5y + 0.5625 + y2 = 0.7083333333 + 0.5625

Reorder the terms:
0.5625 + -1.5y + y2 = 0.7083333333 + 0.5625

Combine like terms: 0.7083333333 + 0.5625 = 1.2708333333
0.5625 + -1.5y + y2 = 1.2708333333

Factor a perfect square on the left side:
(y + -0.75)(y + -0.75) = 1.2708333333

Calculate the square root of the right side: 1.127312438

Break this problem into two subproblems by setting 
(y + -0.75) equal to 1.127312438 and -1.127312438.


Subproblem 1
y + -0.75 = 1.127312438

Simplifying
y + -0.75 = 1.127312438

Reorder the terms:
-0.75 + y = 1.127312438

Solving
-0.75 + y = 1.127312438

Solving for variable 'y'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + y = 1.127312438 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + y = 1.127312438 + 0.75
y = 1.127312438 + 0.75

Combine like terms: 1.127312438 + 0.75 = 1.877312438
y = 1.877312438

Simplifying
y = 1.877312438


Subproblem 2
y + -0.75 = -1.127312438

Simplifying
y + -0.75 = -1.127312438

Reorder the terms:
-0.75 + y = -1.127312438

Solving
-0.75 + y = -1.127312438

Solving for variable 'y'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + y = -1.127312438 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + y = -1.127312438 + 0.75
y = -1.127312438 + 0.75

Combine like terms: -1.127312438 + 0.75 = -0.377312438
y = -0.377312438

Simplifying
y = -0.377312438


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.877312438, -0.377312438}
Solution
y = {1.877312438, -0.377312438}

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