2(3y+6)4(3+2y)=350

Solution for 2(3y+6)4(3+2y)=350 equation:

Simplifying
2(3y + 6) * 4(3 + 2y) = 350

Reorder the terms:
2(6 + 3y) * 4(3 + 2y) = 350

Reorder the terms for easier multiplication:
2 * 4(6 + 3y)(3 + 2y) = 350

Multiply 2 * 4
8(6 + 3y)(3 + 2y) = 350

Multiply (6 + 3y) * (3 + 2y)
8(6(3 + 2y) + 3y * (3 + 2y)) = 350
8((3 * 6 + 2y * 6) + 3y * (3 + 2y)) = 350
8((18 + 12y) + 3y * (3 + 2y)) = 350
8(18 + 12y + (3 * 3y + 2y * 3y)) = 350
8(18 + 12y + (9y + 6y2)) = 350

Combine like terms: 12y + 9y = 21y
8(18 + 21y + 6y2) = 350
(18 * 8 + 21y * 8 + 6y2 * 8) = 350
(144 + 168y + 48y2) = 350

Solving
144 + 168y + 48y2 = 350

Solving for variable 'y'.

Reorder the terms:
144 + -350 + 168y + 48y2 = 350 + -350

Combine like terms: 144 + -350 = -206
-206 + 168y + 48y2 = 350 + -350

Combine like terms: 350 + -350 = 0
-206 + 168y + 48y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-103 + 84y + 24y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-103 + 84y + 24y2)' equal to zero and attempt to solve:

Simplifying
-103 + 84y + 24y2 = 0

Solving
-103 + 84y + 24y2 = 0

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

Divide each side by '24'.
-4.291666667 + 3.5y + y2 = 0

Move the constant term to the right:

Add '4.291666667' to each side of the equation.
-4.291666667 + 3.5y + 4.291666667 + y2 = 0 + 4.291666667

Reorder the terms:
-4.291666667 + 4.291666667 + 3.5y + y2 = 0 + 4.291666667

Combine like terms: -4.291666667 + 4.291666667 = 0.000000000
0.000000000 + 3.5y + y2 = 0 + 4.291666667
3.5y + y2 = 0 + 4.291666667

Combine like terms: 0 + 4.291666667 = 4.291666667
3.5y + y2 = 4.291666667

The y term is 3.5y.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5y + 3.0625 + y2 = 4.291666667 + 3.0625

Reorder the terms:
3.0625 + 3.5y + y2 = 4.291666667 + 3.0625

Combine like terms: 4.291666667 + 3.0625 = 7.354166667
3.0625 + 3.5y + y2 = 7.354166667

Factor a perfect square on the left side:
(y + 1.75)(y + 1.75) = 7.354166667

Calculate the square root of the right side: 2.711856683

Break this problem into two subproblems by setting 
(y + 1.75) equal to 2.711856683 and -2.711856683.

Subproblem 1
y + 1.75 = 2.711856683

Simplifying
y + 1.75 = 2.711856683

Reorder the terms:
1.75 + y = 2.711856683

Solving
1.75 + y = 2.711856683

Solving for variable 'y'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + y = 2.711856683 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + y = 2.711856683 + -1.75
y = 2.711856683 + -1.75

Combine like terms: 2.711856683 + -1.75 = 0.961856683
y = 0.961856683

Simplifying
y = 0.961856683

Subproblem 2
y + 1.75 = -2.711856683

Simplifying
y + 1.75 = -2.711856683

Reorder the terms:
1.75 + y = -2.711856683

Solving
1.75 + y = -2.711856683

Solving for variable 'y'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + y = -2.711856683 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + y = -2.711856683 + -1.75
y = -2.711856683 + -1.75

Combine like terms: -2.711856683 + -1.75 = -4.461856683
y = -4.461856683

Simplifying
y = -4.461856683

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.961856683, -4.461856683}
Solution
y = {0.961856683, -4.461856683}