3(y+1)(-1-3y)=4y-2(y+1)

Solution for 3(y+1)(-1-3y)=4y-2(y+1) equation:

Simplifying
3(y + 1)(-1 + -3y) = 4y + -2(y + 1)

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

Multiply (1 + y) * (-1 + -3y)
3(1(-1 + -3y) + y(-1 + -3y)) = 4y + -2(y + 1)
3((-1 * 1 + -3y * 1) + y(-1 + -3y)) = 4y + -2(y + 1)
3((-1 + -3y) + y(-1 + -3y)) = 4y + -2(y + 1)
3(-1 + -3y + (-1 * y + -3y * y)) = 4y + -2(y + 1)
3(-1 + -3y + (-1y + -3y2)) = 4y + -2(y + 1)

Combine like terms: -3y + -1y = -4y
3(-1 + -4y + -3y2) = 4y + -2(y + 1)
(-1 * 3 + -4y * 3 + -3y2 * 3) = 4y + -2(y + 1)
(-3 + -12y + -9y2) = 4y + -2(y + 1)

Reorder the terms:
-3 + -12y + -9y2 = 4y + -2(1 + y)
-3 + -12y + -9y2 = 4y + (1 * -2 + y * -2)
-3 + -12y + -9y2 = 4y + (-2 + -2y)

Reorder the terms:
-3 + -12y + -9y2 = -2 + 4y + -2y

Combine like terms: 4y + -2y = 2y
-3 + -12y + -9y2 = -2 + 2y

Solving
-3 + -12y + -9y2 = -2 + 2y

Solving for variable 'y'.

Reorder the terms:
-3 + 2 + -12y + -2y + -9y2 = -2 + 2y + 2 + -2y

Combine like terms: -3 + 2 = -1
-1 + -12y + -2y + -9y2 = -2 + 2y + 2 + -2y

Combine like terms: -12y + -2y = -14y
-1 + -14y + -9y2 = -2 + 2y + 2 + -2y

Reorder the terms:
-1 + -14y + -9y2 = -2 + 2 + 2y + -2y

Combine like terms: -2 + 2 = 0
-1 + -14y + -9y2 = 0 + 2y + -2y
-1 + -14y + -9y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-1 + -14y + -9y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 14y + 9y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 14y + 9y2)' equal to zero and attempt to solve:

Simplifying
1 + 14y + 9y2 = 0

Solving
1 + 14y + 9y2 = 0

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

Divide each side by '9'.
0.1111111111 + 1.555555556y + y2 = 0

Move the constant term to the right:

Add '-0.1111111111' to each side of the equation.
0.1111111111 + 1.555555556y + -0.1111111111 + y2 = 0 + -0.1111111111

Reorder the terms:
0.1111111111 + -0.1111111111 + 1.555555556y + y2 = 0 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + 1.555555556y + y2 = 0 + -0.1111111111
1.555555556y + y2 = 0 + -0.1111111111

Combine like terms: 0 + -0.1111111111 = -0.1111111111
1.555555556y + y2 = -0.1111111111

The y term is 1.555555556y.  Take half its coefficient (0.777777778).
Square it (0.6049382720) and add it to both sides.

Add '0.6049382720' to each side of the equation.
1.555555556y + 0.6049382720 + y2 = -0.1111111111 + 0.6049382720

Reorder the terms:
0.6049382720 + 1.555555556y + y2 = -0.1111111111 + 0.6049382720

Combine like terms: -0.1111111111 + 0.6049382720 = 0.4938271609
0.6049382720 + 1.555555556y + y2 = 0.4938271609

Factor a perfect square on the left side:
(y + 0.777777778)(y + 0.777777778) = 0.4938271609

Calculate the square root of the right side: 0.702728369

Break this problem into two subproblems by setting 
(y + 0.777777778) equal to 0.702728369 and -0.702728369.

Subproblem 1
y + 0.777777778 = 0.702728369

Simplifying
y + 0.777777778 = 0.702728369

Reorder the terms:
0.777777778 + y = 0.702728369

Solving
0.777777778 + y = 0.702728369

Solving for variable 'y'.

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

Add '-0.777777778' to each side of the equation.
0.777777778 + -0.777777778 + y = 0.702728369 + -0.777777778

Combine like terms: 0.777777778 + -0.777777778 = 0.000000000
0.000000000 + y = 0.702728369 + -0.777777778
y = 0.702728369 + -0.777777778

Combine like terms: 0.702728369 + -0.777777778 = -0.075049409
y = -0.075049409

Simplifying
y = -0.075049409

Subproblem 2
y + 0.777777778 = -0.702728369

Simplifying
y + 0.777777778 = -0.702728369

Reorder the terms:
0.777777778 + y = -0.702728369

Solving
0.777777778 + y = -0.702728369

Solving for variable 'y'.

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

Add '-0.777777778' to each side of the equation.
0.777777778 + -0.777777778 + y = -0.702728369 + -0.777777778

Combine like terms: 0.777777778 + -0.777777778 = 0.000000000
0.000000000 + y = -0.702728369 + -0.777777778
y = -0.702728369 + -0.777777778

Combine like terms: -0.702728369 + -0.777777778 = -1.480506147
y = -1.480506147

Simplifying
y = -1.480506147

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.075049409, -1.480506147}
Solution
y = {-0.075049409, -1.480506147}