(9y+2)*(4y-8)=6y^2-24y+4

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Solution for (9y+2)*(4y-8)=6y^2-24y+4 equation: 


Simplifying
(9y + 2)(4y + -8) = 6y2 + -24y + 4

Reorder the terms:
(2 + 9y)(4y + -8) = 6y2 + -24y + 4

Reorder the terms:
(2 + 9y)(-8 + 4y) = 6y2 + -24y + 4

Multiply (2 + 9y) * (-8 + 4y)
(2(-8 + 4y) + 9y * (-8 + 4y)) = 6y2 + -24y + 4
((-8 * 2 + 4y * 2) + 9y * (-8 + 4y)) = 6y2 + -24y + 4
((-16 + 8y) + 9y * (-8 + 4y)) = 6y2 + -24y + 4
(-16 + 8y + (-8 * 9y + 4y * 9y)) = 6y2 + -24y + 4
(-16 + 8y + (-72y + 36y2)) = 6y2 + -24y + 4

Combine like terms: 8y + -72y = -64y
(-16 + -64y + 36y2) = 6y2 + -24y + 4

Reorder the terms:
-16 + -64y + 36y2 = 4 + -24y + 6y2

Solving
-16 + -64y + 36y2 = 4 + -24y + 6y2

Solving for variable 'y'.

Reorder the terms:
-16 + -4 + -64y + 24y + 36y2 + -6y2 = 4 + -24y + 6y2 + -4 + 24y + -6y2

Combine like terms: -16 + -4 = -20
-20 + -64y + 24y + 36y2 + -6y2 = 4 + -24y + 6y2 + -4 + 24y + -6y2

Combine like terms: -64y + 24y = -40y
-20 + -40y + 36y2 + -6y2 = 4 + -24y + 6y2 + -4 + 24y + -6y2

Combine like terms: 36y2 + -6y2 = 30y2
-20 + -40y + 30y2 = 4 + -24y + 6y2 + -4 + 24y + -6y2

Reorder the terms:
-20 + -40y + 30y2 = 4 + -4 + -24y + 24y + 6y2 + -6y2

Combine like terms: 4 + -4 = 0
-20 + -40y + 30y2 = 0 + -24y + 24y + 6y2 + -6y2
-20 + -40y + 30y2 = -24y + 24y + 6y2 + -6y2

Combine like terms: -24y + 24y = 0
-20 + -40y + 30y2 = 0 + 6y2 + -6y2
-20 + -40y + 30y2 = 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
-20 + -40y + 30y2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-2 + -4y + 3y2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-2 + -4y + 3y2)' equal to zero and attempt to solve:

Simplifying
-2 + -4y + 3y2 = 0

Solving
-2 + -4y + 3y2 = 0

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

Divide each side by '3'.
-0.6666666667 + -1.333333333y + y2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -1.333333333y + 0.6666666667 + y2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -1.333333333y + y2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -1.333333333y + y2 = 0 + 0.6666666667
-1.333333333y + y2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-1.333333333y + y2 = 0.6666666667

The y term is -1.333333333y.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333y + 0.4444444442 + y2 = 0.6666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333y + y2 = 0.6666666667 + 0.4444444442

Combine like terms: 0.6666666667 + 0.4444444442 = 1.1111111109
0.4444444442 + -1.333333333y + y2 = 1.1111111109

Factor a perfect square on the left side:
(y + -0.6666666665)(y + -0.6666666665) = 1.1111111109

Calculate the square root of the right side: 1.054092553

Break this problem into two subproblems by setting 
(y + -0.6666666665) equal to 1.054092553 and -1.054092553.


Subproblem 1
y + -0.6666666665 = 1.054092553

Simplifying
y + -0.6666666665 = 1.054092553

Reorder the terms:
-0.6666666665 + y = 1.054092553

Solving
-0.6666666665 + y = 1.054092553

Solving for variable 'y'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + y = 1.054092553 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + y = 1.054092553 + 0.6666666665
y = 1.054092553 + 0.6666666665

Combine like terms: 1.054092553 + 0.6666666665 = 1.7207592195
y = 1.7207592195

Simplifying
y = 1.7207592195


Subproblem 2
y + -0.6666666665 = -1.054092553

Simplifying
y + -0.6666666665 = -1.054092553

Reorder the terms:
-0.6666666665 + y = -1.054092553

Solving
-0.6666666665 + y = -1.054092553

Solving for variable 'y'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + y = -1.054092553 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + y = -1.054092553 + 0.6666666665
y = -1.054092553 + 0.6666666665

Combine like terms: -1.054092553 + 0.6666666665 = -0.3874258865
y = -0.3874258865

Simplifying
y = -0.3874258865


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.7207592195, -0.3874258865}
Solution
y = {1.7207592195, -0.3874258865}

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