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

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

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

Reorder the terms:
7(-2 + 3y) + -6 = -3y(1 + -1y)
(-2 * 7 + 3y * 7) + -6 = -3y(1 + -1y)
(-14 + 21y) + -6 = -3y(1 + -1y)

Reorder the terms:
-14 + -6 + 21y = -3y(1 + -1y)

Combine like terms: -14 + -6 = -20
-20 + 21y = -3y(1 + -1y)
-20 + 21y = (1 * -3y + -1y * -3y)
-20 + 21y = (-3y + 3y2)

Solving
-20 + 21y = -3y + 3y2

Solving for variable 'y'.

Combine like terms: 21y + 3y = 24y
-20 + 24y + -3y2 = -3y + 3y2 + 3y + -3y2

Reorder the terms:
-20 + 24y + -3y2 = -3y + 3y + 3y2 + -3y2

Combine like terms: -3y + 3y = 0
-20 + 24y + -3y2 = 0 + 3y2 + -3y2
-20 + 24y + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-20 + 24y + -3y2 = 0

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

Divide each side by '-3'.
6.666666667 + -8y + y2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -8y + -6.666666667 + y2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -8y + y2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -8y + y2 = 0 + -6.666666667
-8y + y2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-8y + y2 = -6.666666667

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = -6.666666667 + 16

Reorder the terms:
16 + -8y + y2 = -6.666666667 + 16

Combine like terms: -6.666666667 + 16 = 9.333333333
16 + -8y + y2 = 9.333333333

Factor a perfect square on the left side:
(y + -4)(y + -4) = 9.333333333

Calculate the square root of the right side: 3.055050463

Break this problem into two subproblems by setting 
(y + -4) equal to 3.055050463 and -3.055050463.

Subproblem 1
y + -4 = 3.055050463

Simplifying
y + -4 = 3.055050463

Reorder the terms:
-4 + y = 3.055050463

Solving
-4 + y = 3.055050463

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 3.055050463 + 4

Combine like terms: -4 + 4 = 0
0 + y = 3.055050463 + 4
y = 3.055050463 + 4

Combine like terms: 3.055050463 + 4 = 7.055050463
y = 7.055050463

Simplifying
y = 7.055050463

Subproblem 2
y + -4 = -3.055050463

Simplifying
y + -4 = -3.055050463

Reorder the terms:
-4 + y = -3.055050463

Solving
-4 + y = -3.055050463

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -3.055050463 + 4

Combine like terms: -4 + 4 = 0
0 + y = -3.055050463 + 4
y = -3.055050463 + 4

Combine like terms: -3.055050463 + 4 = 0.944949537
y = 0.944949537

Simplifying
y = 0.944949537

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.055050463, 0.944949537}