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

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

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

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

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

Multiply 7 * 3
21y(-1 + 2y) = 3(y + 2) + 9
(-1 * 21y + 2y * 21y) = 3(y + 2) + 9
(-21y + 42y2) = 3(y + 2) + 9

Reorder the terms:
-21y + 42y2 = 3(2 + y) + 9
-21y + 42y2 = (2 * 3 + y * 3) + 9
-21y + 42y2 = (6 + 3y) + 9

Reorder the terms:
-21y + 42y2 = 6 + 9 + 3y

Combine like terms: 6 + 9 = 15
-21y + 42y2 = 15 + 3y

Solving
-21y + 42y2 = 15 + 3y

Solving for variable 'y'.

Reorder the terms:
-15 + -21y + -3y + 42y2 = 15 + 3y + -15 + -3y

Combine like terms: -21y + -3y = -24y
-15 + -24y + 42y2 = 15 + 3y + -15 + -3y

Reorder the terms:
-15 + -24y + 42y2 = 15 + -15 + 3y + -3y

Combine like terms: 15 + -15 = 0
-15 + -24y + 42y2 = 0 + 3y + -3y
-15 + -24y + 42y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-15 + -24y + 42y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -8y + 14y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -8y + 14y2)' equal to zero and attempt to solve:

Simplifying
-5 + -8y + 14y2 = 0

Solving
-5 + -8y + 14y2 = 0

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

Divide each side by '14'.
-0.3571428571 + -0.5714285714y + y2 = 0

Move the constant term to the right:

Add '0.3571428571' to each side of the equation.
-0.3571428571 + -0.5714285714y + 0.3571428571 + y2 = 0 + 0.3571428571

Reorder the terms:
-0.3571428571 + 0.3571428571 + -0.5714285714y + y2 = 0 + 0.3571428571

Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000
0.0000000000 + -0.5714285714y + y2 = 0 + 0.3571428571
-0.5714285714y + y2 = 0 + 0.3571428571

Combine like terms: 0 + 0.3571428571 = 0.3571428571
-0.5714285714y + y2 = 0.3571428571

The y term is -0.5714285714y.  Take half its coefficient (-0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
-0.5714285714y + 0.08163265305 + y2 = 0.3571428571 + 0.08163265305

Reorder the terms:
0.08163265305 + -0.5714285714y + y2 = 0.3571428571 + 0.08163265305

Combine like terms: 0.3571428571 + 0.08163265305 = 0.43877551015
0.08163265305 + -0.5714285714y + y2 = 0.43877551015

Factor a perfect square on the left side:
(y + -0.2857142857)(y + -0.2857142857) = 0.43877551015

Calculate the square root of the right side: 0.662401321

Break this problem into two subproblems by setting 
(y + -0.2857142857) equal to 0.662401321 and -0.662401321.

Subproblem 1
y + -0.2857142857 = 0.662401321

Simplifying
y + -0.2857142857 = 0.662401321

Reorder the terms:
-0.2857142857 + y = 0.662401321

Solving
-0.2857142857 + y = 0.662401321

Solving for variable 'y'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + y = 0.662401321 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + y = 0.662401321 + 0.2857142857
y = 0.662401321 + 0.2857142857

Combine like terms: 0.662401321 + 0.2857142857 = 0.9481156067
y = 0.9481156067

Simplifying
y = 0.9481156067

Subproblem 2
y + -0.2857142857 = -0.662401321

Simplifying
y + -0.2857142857 = -0.662401321

Reorder the terms:
-0.2857142857 + y = -0.662401321

Solving
-0.2857142857 + y = -0.662401321

Solving for variable 'y'.

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

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 0.2857142857 + y = -0.662401321 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + y = -0.662401321 + 0.2857142857
y = -0.662401321 + 0.2857142857

Combine like terms: -0.662401321 + 0.2857142857 = -0.3766870353
y = -0.3766870353

Simplifying
y = -0.3766870353

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.9481156067, -0.3766870353}
Solution
y = {0.9481156067, -0.3766870353}