7(2y-1)+3y=-3y(y+2+9)

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Solution for 7(2y-1)+3y=-3y(y+2+9) equation: 


Simplifying
7(2y + -1) + 3y = -3y(y + 2 + 9)

Reorder the terms:
7(-1 + 2y) + 3y = -3y(y + 2 + 9)
(-1 * 7 + 2y * 7) + 3y = -3y(y + 2 + 9)
(-7 + 14y) + 3y = -3y(y + 2 + 9)

Combine like terms: 14y + 3y = 17y
-7 + 17y = -3y(y + 2 + 9)

Reorder the terms:
-7 + 17y = -3y(2 + 9 + y)

Combine like terms: 2 + 9 = 11
-7 + 17y = -3y(11 + y)
-7 + 17y = (11 * -3y + y * -3y)
-7 + 17y = (-33y + -3y2)

Solving
-7 + 17y = -33y + -3y2

Solving for variable 'y'.

Combine like terms: 17y + 33y = 50y
-7 + 50y + 3y2 = -33y + -3y2 + 33y + 3y2

Reorder the terms:
-7 + 50y + 3y2 = -33y + 33y + -3y2 + 3y2

Combine like terms: -33y + 33y = 0
-7 + 50y + 3y2 = 0 + -3y2 + 3y2
-7 + 50y + 3y2 = -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
-7 + 50y + 3y2 = 0

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

Divide each side by '3'.
-2.333333333 + 16.66666667y + y2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 16.66666667y + 2.333333333 + y2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 16.66666667y + y2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 16.66666667y + y2 = 0 + 2.333333333
16.66666667y + y2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
16.66666667y + y2 = 2.333333333

The y term is 16.66666667y.  Take half its coefficient (8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
16.66666667y + 69.44444447 + y2 = 2.333333333 + 69.44444447

Reorder the terms:
69.44444447 + 16.66666667y + y2 = 2.333333333 + 69.44444447

Combine like terms: 2.333333333 + 69.44444447 = 71.777777803
69.44444447 + 16.66666667y + y2 = 71.777777803

Factor a perfect square on the left side:
(y + 8.333333335)(y + 8.333333335) = 71.777777803

Calculate the square root of the right side: 8.472176686

Break this problem into two subproblems by setting 
(y + 8.333333335) equal to 8.472176686 and -8.472176686.


Subproblem 1
y + 8.333333335 = 8.472176686

Simplifying
y + 8.333333335 = 8.472176686

Reorder the terms:
8.333333335 + y = 8.472176686

Solving
8.333333335 + y = 8.472176686

Solving for variable 'y'.

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

Add '-8.333333335' to each side of the equation.
8.333333335 + -8.333333335 + y = 8.472176686 + -8.333333335

Combine like terms: 8.333333335 + -8.333333335 = 0.000000000
0.000000000 + y = 8.472176686 + -8.333333335
y = 8.472176686 + -8.333333335

Combine like terms: 8.472176686 + -8.333333335 = 0.138843351
y = 0.138843351

Simplifying
y = 0.138843351


Subproblem 2
y + 8.333333335 = -8.472176686

Simplifying
y + 8.333333335 = -8.472176686

Reorder the terms:
8.333333335 + y = -8.472176686

Solving
8.333333335 + y = -8.472176686

Solving for variable 'y'.

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

Add '-8.333333335' to each side of the equation.
8.333333335 + -8.333333335 + y = -8.472176686 + -8.333333335

Combine like terms: 8.333333335 + -8.333333335 = 0.000000000
0.000000000 + y = -8.472176686 + -8.333333335
y = -8.472176686 + -8.333333335

Combine like terms: -8.472176686 + -8.333333335 = -16.805510021
y = -16.805510021

Simplifying
y = -16.805510021


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.138843351, -16.805510021}

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