-2y(3y-6)+4(5y-8)=92

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Solution for -2y(3y-6)+4(5y-8)=92 equation:


Simplifying
-2y(3y + -6) + 4(5y + -8) = 92

Reorder the terms:
-2y(-6 + 3y) + 4(5y + -8) = 92
(-6 * -2y + 3y * -2y) + 4(5y + -8) = 92
(12y + -6y2) + 4(5y + -8) = 92

Reorder the terms:
12y + -6y2 + 4(-8 + 5y) = 92
12y + -6y2 + (-8 * 4 + 5y * 4) = 92
12y + -6y2 + (-32 + 20y) = 92

Reorder the terms:
-32 + 12y + 20y + -6y2 = 92

Combine like terms: 12y + 20y = 32y
-32 + 32y + -6y2 = 92

Solving
-32 + 32y + -6y2 = 92

Solving for variable 'y'.

Reorder the terms:
-32 + -92 + 32y + -6y2 = 92 + -92

Combine like terms: -32 + -92 = -124
-124 + 32y + -6y2 = 92 + -92

Combine like terms: 92 + -92 = 0
-124 + 32y + -6y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-62 + 16y + -3y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-62 + 16y + -3y2)' equal to zero and attempt to solve:

Simplifying
-62 + 16y + -3y2 = 0

Solving
-62 + 16y + -3y2 = 0

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

Divide each side by '-3'.
20.66666667 + -5.333333333y + y2 = 0

Move the constant term to the right:

Add '-20.66666667' to each side of the equation.
20.66666667 + -5.333333333y + -20.66666667 + y2 = 0 + -20.66666667

Reorder the terms:
20.66666667 + -20.66666667 + -5.333333333y + y2 = 0 + -20.66666667

Combine like terms: 20.66666667 + -20.66666667 = 0.00000000
0.00000000 + -5.333333333y + y2 = 0 + -20.66666667
-5.333333333y + y2 = 0 + -20.66666667

Combine like terms: 0 + -20.66666667 = -20.66666667
-5.333333333y + y2 = -20.66666667

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 = -20.66666667 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333y + y2 = -20.66666667 + 7.111111113

Combine like terms: -20.66666667 + 7.111111113 = -13.555555557
7.111111113 + -5.333333333y + y2 = -13.555555557

Factor a perfect square on the left side:
(y + -2.666666667)(y + -2.666666667) = -13.555555557

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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