6y+3(1-y)=7(y-2)3y

Solution for 6y+3(1-y)=7(y-2)3y equation:

Simplifying
6y + 3(1 + -1y) = 7(y + -2) * 3y
6y + (1 * 3 + -1y * 3) = 7(y + -2) * 3y
6y + (3 + -3y) = 7(y + -2) * 3y

Reorder the terms:
3 + 6y + -3y = 7(y + -2) * 3y

Combine like terms: 6y + -3y = 3y
3 + 3y = 7(y + -2) * 3y

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

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

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

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

Solving for variable 'y'.

Combine like terms: 3y + 42y = 45y
3 + 45y + -21y2 = -42y + 21y2 + 42y + -21y2

Reorder the terms:
3 + 45y + -21y2 = -42y + 42y + 21y2 + -21y2

Combine like terms: -42y + 42y = 0
3 + 45y + -21y2 = 0 + 21y2 + -21y2
3 + 45y + -21y2 = 21y2 + -21y2

Combine like terms: 21y2 + -21y2 = 0
3 + 45y + -21y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 15y + -7y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + 15y + -7y2)' equal to zero and attempt to solve:

Simplifying
1 + 15y + -7y2 = 0

Solving
1 + 15y + -7y2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.1428571429 + -2.142857143y + y2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + -2.142857143y + 0.1428571429 + y2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + -2.142857143y + y2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + -2.142857143y + y2 = 0 + 0.1428571429
-2.142857143y + y2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
-2.142857143y + y2 = 0.1428571429

The y term is -2.142857143y.  Take half its coefficient (-1.071428572).
Square it (1.147959185) and add it to both sides.

Add '1.147959185' to each side of the equation.
-2.142857143y + 1.147959185 + y2 = 0.1428571429 + 1.147959185

Reorder the terms:
1.147959185 + -2.142857143y + y2 = 0.1428571429 + 1.147959185

Combine like terms: 0.1428571429 + 1.147959185 = 1.2908163279
1.147959185 + -2.142857143y + y2 = 1.2908163279

Factor a perfect square on the left side:
(y + -1.071428572)(y + -1.071428572) = 1.2908163279

Calculate the square root of the right side: 1.136140981

Break this problem into two subproblems by setting 
(y + -1.071428572) equal to 1.136140981 and -1.136140981.

Subproblem 1
y + -1.071428572 = 1.136140981

Simplifying
y + -1.071428572 = 1.136140981

Reorder the terms:
-1.071428572 + y = 1.136140981

Solving
-1.071428572 + y = 1.136140981

Solving for variable 'y'.

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

Add '1.071428572' to each side of the equation.
-1.071428572 + 1.071428572 + y = 1.136140981 + 1.071428572

Combine like terms: -1.071428572 + 1.071428572 = 0.000000000
0.000000000 + y = 1.136140981 + 1.071428572
y = 1.136140981 + 1.071428572

Combine like terms: 1.136140981 + 1.071428572 = 2.207569553
y = 2.207569553

Simplifying
y = 2.207569553

Subproblem 2
y + -1.071428572 = -1.136140981

Simplifying
y + -1.071428572 = -1.136140981

Reorder the terms:
-1.071428572 + y = -1.136140981

Solving
-1.071428572 + y = -1.136140981

Solving for variable 'y'.

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

Add '1.071428572' to each side of the equation.
-1.071428572 + 1.071428572 + y = -1.136140981 + 1.071428572

Combine like terms: -1.071428572 + 1.071428572 = 0.000000000
0.000000000 + y = -1.136140981 + 1.071428572
y = -1.136140981 + 1.071428572

Combine like terms: -1.136140981 + 1.071428572 = -0.064712409
y = -0.064712409

Simplifying
y = -0.064712409

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.207569553, -0.064712409}
Solution
y = {2.207569553, -0.064712409}