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

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 + y) + 9
-7 + 17y = (2 * -3y + y * -3y) + 9
-7 + 17y = (-6y + -3y2) + 9

Reorder the terms:
-7 + 17y = 9 + -6y + -3y2

Solving
-7 + 17y = 9 + -6y + -3y2

Solving for variable 'y'.

Reorder the terms:
-7 + -9 + 17y + 6y + 3y2 = 9 + -6y + -3y2 + -9 + 6y + 3y2

Combine like terms: -7 + -9 = -16
-16 + 17y + 6y + 3y2 = 9 + -6y + -3y2 + -9 + 6y + 3y2

Combine like terms: 17y + 6y = 23y
-16 + 23y + 3y2 = 9 + -6y + -3y2 + -9 + 6y + 3y2

Reorder the terms:
-16 + 23y + 3y2 = 9 + -9 + -6y + 6y + -3y2 + 3y2

Combine like terms: 9 + -9 = 0
-16 + 23y + 3y2 = 0 + -6y + 6y + -3y2 + 3y2
-16 + 23y + 3y2 = -6y + 6y + -3y2 + 3y2

Combine like terms: -6y + 6y = 0
-16 + 23y + 3y2 = 0 + -3y2 + 3y2
-16 + 23y + 3y2 = -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
-16 + 23y + 3y2 = 0

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

Divide each side by '3'.
-5.333333333 + 7.666666667y + y2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + 7.666666667y + 5.333333333 + y2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + 7.666666667y + y2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + 7.666666667y + y2 = 0 + 5.333333333
7.666666667y + y2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
7.666666667y + y2 = 5.333333333

The y term is 7.666666667y.  Take half its coefficient (3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
7.666666667y + 14.69444445 + y2 = 5.333333333 + 14.69444445

Reorder the terms:
14.69444445 + 7.666666667y + y2 = 5.333333333 + 14.69444445

Combine like terms: 5.333333333 + 14.69444445 = 20.027777783
14.69444445 + 7.666666667y + y2 = 20.027777783

Factor a perfect square on the left side:
(y + 3.833333334)(y + 3.833333334) = 20.027777783

Calculate the square root of the right side: 4.475240528

Break this problem into two subproblems by setting 
(y + 3.833333334) equal to 4.475240528 and -4.475240528.

Subproblem 1
y + 3.833333334 = 4.475240528

Simplifying
y + 3.833333334 = 4.475240528

Reorder the terms:
3.833333334 + y = 4.475240528

Solving
3.833333334 + y = 4.475240528

Solving for variable 'y'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + y = 4.475240528 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + y = 4.475240528 + -3.833333334
y = 4.475240528 + -3.833333334

Combine like terms: 4.475240528 + -3.833333334 = 0.641907194
y = 0.641907194

Simplifying
y = 0.641907194

Subproblem 2
y + 3.833333334 = -4.475240528

Simplifying
y + 3.833333334 = -4.475240528

Reorder the terms:
3.833333334 + y = -4.475240528

Solving
3.833333334 + y = -4.475240528

Solving for variable 'y'.

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

Add '-3.833333334' to each side of the equation.
3.833333334 + -3.833333334 + y = -4.475240528 + -3.833333334

Combine like terms: 3.833333334 + -3.833333334 = 0.000000000
0.000000000 + y = -4.475240528 + -3.833333334
y = -4.475240528 + -3.833333334

Combine like terms: -4.475240528 + -3.833333334 = -8.308573862
y = -8.308573862

Simplifying
y = -8.308573862

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.641907194, -8.308573862}