7(y-3)5=4(2-y)3y

Solution for 7(y-3)5=4(2-y)3y equation:

Simplifying
7(y + -3) * 5 = 4(2 + -1y) * 3y

Reorder the terms:
7(-3 + y) * 5 = 4(2 + -1y) * 3y

Reorder the terms for easier multiplication:
7 * 5(-3 + y) = 4(2 + -1y) * 3y

Multiply 7 * 5
35(-3 + y) = 4(2 + -1y) * 3y
(-3 * 35 + y * 35) = 4(2 + -1y) * 3y
(-105 + 35y) = 4(2 + -1y) * 3y

Reorder the terms for easier multiplication:
-105 + 35y = 4 * 3y(2 + -1y)

Multiply 4 * 3
-105 + 35y = 12y(2 + -1y)
-105 + 35y = (2 * 12y + -1y * 12y)
-105 + 35y = (24y + -12y2)

Solving
-105 + 35y = 24y + -12y2

Solving for variable 'y'.

Combine like terms: 35y + -24y = 11y
-105 + 11y + 12y2 = 24y + -12y2 + -24y + 12y2

Reorder the terms:
-105 + 11y + 12y2 = 24y + -24y + -12y2 + 12y2

Combine like terms: 24y + -24y = 0
-105 + 11y + 12y2 = 0 + -12y2 + 12y2
-105 + 11y + 12y2 = -12y2 + 12y2

Combine like terms: -12y2 + 12y2 = 0
-105 + 11y + 12y2 = 0

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

Divide each side by '12'.
-8.75 + 0.9166666667y + y2 = 0

Move the constant term to the right:

Add '8.75' to each side of the equation.
-8.75 + 0.9166666667y + 8.75 + y2 = 0 + 8.75

Reorder the terms:
-8.75 + 8.75 + 0.9166666667y + y2 = 0 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + 0.9166666667y + y2 = 0 + 8.75
0.9166666667y + y2 = 0 + 8.75

Combine like terms: 0 + 8.75 = 8.75
0.9166666667y + y2 = 8.75

The y term is 0.9166666667y.  Take half its coefficient (0.4583333334).
Square it (0.2100694445) and add it to both sides.

Add '0.2100694445' to each side of the equation.
0.9166666667y + 0.2100694445 + y2 = 8.75 + 0.2100694445

Reorder the terms:
0.2100694445 + 0.9166666667y + y2 = 8.75 + 0.2100694445

Combine like terms: 8.75 + 0.2100694445 = 8.9600694445
0.2100694445 + 0.9166666667y + y2 = 8.9600694445

Factor a perfect square on the left side:
(y + 0.4583333334)(y + 0.4583333334) = 8.9600694445

Calculate the square root of the right side: 2.993337509

Break this problem into two subproblems by setting 
(y + 0.4583333334) equal to 2.993337509 and -2.993337509.

Subproblem 1
y + 0.4583333334 = 2.993337509

Simplifying
y + 0.4583333334 = 2.993337509

Reorder the terms:
0.4583333334 + y = 2.993337509

Solving
0.4583333334 + y = 2.993337509

Solving for variable 'y'.

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

Add '-0.4583333334' to each side of the equation.
0.4583333334 + -0.4583333334 + y = 2.993337509 + -0.4583333334

Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000
0.0000000000 + y = 2.993337509 + -0.4583333334
y = 2.993337509 + -0.4583333334

Combine like terms: 2.993337509 + -0.4583333334 = 2.5350041756
y = 2.5350041756

Simplifying
y = 2.5350041756

Subproblem 2
y + 0.4583333334 = -2.993337509

Simplifying
y + 0.4583333334 = -2.993337509

Reorder the terms:
0.4583333334 + y = -2.993337509

Solving
0.4583333334 + y = -2.993337509

Solving for variable 'y'.

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

Add '-0.4583333334' to each side of the equation.
0.4583333334 + -0.4583333334 + y = -2.993337509 + -0.4583333334

Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000
0.0000000000 + y = -2.993337509 + -0.4583333334
y = -2.993337509 + -0.4583333334

Combine like terms: -2.993337509 + -0.4583333334 = -3.4516708424
y = -3.4516708424

Simplifying
y = -3.4516708424

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.5350041756, -3.4516708424}