3y-(2y+7)(8+3y)=

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Solution for 3y-(2y+7)(8+3y)= equation: 


Simplifying
3y + -1(2y + 7)(8 + 3y) = 0

Reorder the terms:
3y + -1(7 + 2y)(8 + 3y) = 0

Multiply (7 + 2y) * (8 + 3y)
3y + -1(7(8 + 3y) + 2y * (8 + 3y)) = 0
3y + -1((8 * 7 + 3y * 7) + 2y * (8 + 3y)) = 0
3y + -1((56 + 21y) + 2y * (8 + 3y)) = 0
3y + -1(56 + 21y + (8 * 2y + 3y * 2y)) = 0
3y + -1(56 + 21y + (16y + 6y2)) = 0

Combine like terms: 21y + 16y = 37y
3y + -1(56 + 37y + 6y2) = 0
3y + (56 * -1 + 37y * -1 + 6y2 * -1) = 0
3y + (-56 + -37y + -6y2) = 0

Reorder the terms:
-56 + 3y + -37y + -6y2 = 0

Combine like terms: 3y + -37y = -34y
-56 + -34y + -6y2 = 0

Solving
-56 + -34y + -6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(28 + 17y + 3y2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(28 + 17y + 3y2)' equal to zero and attempt to solve:

Simplifying
28 + 17y + 3y2 = 0

Solving
28 + 17y + 3y2 = 0

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

Divide each side by '3'.
9.333333333 + 5.666666667y + y2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + 5.666666667y + -9.333333333 + y2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + 5.666666667y + y2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + 5.666666667y + y2 = 0 + -9.333333333
5.666666667y + y2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
5.666666667y + y2 = -9.333333333

The y term is 5.666666667y.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667y + 8.027777782 + y2 = -9.333333333 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667y + y2 = -9.333333333 + 8.027777782

Combine like terms: -9.333333333 + 8.027777782 = -1.305555551
8.027777782 + 5.666666667y + y2 = -1.305555551

Factor a perfect square on the left side:
(y + 2.833333334)(y + 2.833333334) = -1.305555551

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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