-3(-4-6y)7(-y+5)=-8

Solution for -3(-4-6y)7(-y+5)=-8 equation:

Simplifying
-3(-4 + -6y) * 7(-1y + 5) = -8

Reorder the terms:
-3(-4 + -6y) * 7(5 + -1y) = -8

Reorder the terms for easier multiplication:
-3 * 7(-4 + -6y)(5 + -1y) = -8

Multiply -3 * 7
-21(-4 + -6y)(5 + -1y) = -8

Multiply (-4 + -6y) * (5 + -1y)
-21(-4(5 + -1y) + -6y * (5 + -1y)) = -8
-21((5 * -4 + -1y * -4) + -6y * (5 + -1y)) = -8
-21((-20 + 4y) + -6y * (5 + -1y)) = -8
-21(-20 + 4y + (5 * -6y + -1y * -6y)) = -8
-21(-20 + 4y + (-30y + 6y2)) = -8

Combine like terms: 4y + -30y = -26y
-21(-20 + -26y + 6y2) = -8
(-20 * -21 + -26y * -21 + 6y2 * -21) = -8
(420 + 546y + -126y2) = -8

Solving
420 + 546y + -126y2 = -8

Solving for variable 'y'.

Reorder the terms:
420 + 8 + 546y + -126y2 = -8 + 8

Combine like terms: 420 + 8 = 428
428 + 546y + -126y2 = -8 + 8

Combine like terms: -8 + 8 = 0
428 + 546y + -126y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(214 + 273y + -63y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(214 + 273y + -63y2)' equal to zero and attempt to solve:

Simplifying
214 + 273y + -63y2 = 0

Solving
214 + 273y + -63y2 = 0

Begin completing the square.  Divide all terms by
-63 the coefficient of the squared term: 

Divide each side by '-63'.
-3.396825397 + -4.333333333y + y2 = 0

Move the constant term to the right:

Add '3.396825397' to each side of the equation.
-3.396825397 + -4.333333333y + 3.396825397 + y2 = 0 + 3.396825397

Reorder the terms:
-3.396825397 + 3.396825397 + -4.333333333y + y2 = 0 + 3.396825397

Combine like terms: -3.396825397 + 3.396825397 = 0.000000000
0.000000000 + -4.333333333y + y2 = 0 + 3.396825397
-4.333333333y + y2 = 0 + 3.396825397

Combine like terms: 0 + 3.396825397 = 3.396825397
-4.333333333y + y2 = 3.396825397

The y term is -4.333333333y.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333y + 4.694444446 + y2 = 3.396825397 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333y + y2 = 3.396825397 + 4.694444446

Combine like terms: 3.396825397 + 4.694444446 = 8.091269843
4.694444446 + -4.333333333y + y2 = 8.091269843

Factor a perfect square on the left side:
(y + -2.166666667)(y + -2.166666667) = 8.091269843

Calculate the square root of the right side: 2.844515748

Break this problem into two subproblems by setting 
(y + -2.166666667) equal to 2.844515748 and -2.844515748.

Subproblem 1
y + -2.166666667 = 2.844515748

Simplifying
y + -2.166666667 = 2.844515748

Reorder the terms:
-2.166666667 + y = 2.844515748

Solving
-2.166666667 + y = 2.844515748

Solving for variable 'y'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + y = 2.844515748 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + y = 2.844515748 + 2.166666667
y = 2.844515748 + 2.166666667

Combine like terms: 2.844515748 + 2.166666667 = 5.011182415
y = 5.011182415

Simplifying
y = 5.011182415

Subproblem 2
y + -2.166666667 = -2.844515748

Simplifying
y + -2.166666667 = -2.844515748

Reorder the terms:
-2.166666667 + y = -2.844515748

Solving
-2.166666667 + y = -2.844515748

Solving for variable 'y'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + y = -2.844515748 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + y = -2.844515748 + 2.166666667
y = -2.844515748 + 2.166666667

Combine like terms: -2.844515748 + 2.166666667 = -0.677849081
y = -0.677849081

Simplifying
y = -0.677849081

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.011182415, -0.677849081}
Solution
y = {5.011182415, -0.677849081}