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

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

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

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

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

Multiply -6 * 7
-42y(4 + 6y) = -8
(4 * -42y + 6y * -42y) = -8
(-168y + -252y2) = -8

Solving
-168y + -252y2 = -8

Solving for variable 'y'.

Reorder the terms:
8 + -168y + -252y2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + -168y + -252y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -42y + -63y2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -42y + -63y2)' equal to zero and attempt to solve:

Simplifying
2 + -42y + -63y2 = 0

Solving
2 + -42y + -63y2 = 0

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

Divide each side by '-63'.
-0.03174603175 + 0.6666666667y + y2 = 0

Move the constant term to the right:

Add '0.03174603175' to each side of the equation.
-0.03174603175 + 0.6666666667y + 0.03174603175 + y2 = 0 + 0.03174603175

Reorder the terms:
-0.03174603175 + 0.03174603175 + 0.6666666667y + y2 = 0 + 0.03174603175

Combine like terms: -0.03174603175 + 0.03174603175 = 0.00000000000
0.00000000000 + 0.6666666667y + y2 = 0 + 0.03174603175
0.6666666667y + y2 = 0 + 0.03174603175

Combine like terms: 0 + 0.03174603175 = 0.03174603175
0.6666666667y + y2 = 0.03174603175

The y term is 0.6666666667y.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667y + 0.1111111112 + y2 = 0.03174603175 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667y + y2 = 0.03174603175 + 0.1111111112

Combine like terms: 0.03174603175 + 0.1111111112 = 0.14285714295
0.1111111112 + 0.6666666667y + y2 = 0.14285714295

Factor a perfect square on the left side:
(y + 0.3333333334)(y + 0.3333333334) = 0.14285714295

Calculate the square root of the right side: 0.377964473

Break this problem into two subproblems by setting 
(y + 0.3333333334) equal to 0.377964473 and -0.377964473.

Subproblem 1
y + 0.3333333334 = 0.377964473

Simplifying
y + 0.3333333334 = 0.377964473

Reorder the terms:
0.3333333334 + y = 0.377964473

Solving
0.3333333334 + y = 0.377964473

Solving for variable 'y'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + y = 0.377964473 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + y = 0.377964473 + -0.3333333334
y = 0.377964473 + -0.3333333334

Combine like terms: 0.377964473 + -0.3333333334 = 0.0446311396
y = 0.0446311396

Simplifying
y = 0.0446311396

Subproblem 2
y + 0.3333333334 = -0.377964473

Simplifying
y + 0.3333333334 = -0.377964473

Reorder the terms:
0.3333333334 + y = -0.377964473

Solving
0.3333333334 + y = -0.377964473

Solving for variable 'y'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + y = -0.377964473 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + y = -0.377964473 + -0.3333333334
y = -0.377964473 + -0.3333333334

Combine like terms: -0.377964473 + -0.3333333334 = -0.7112978064
y = -0.7112978064

Simplifying
y = -0.7112978064

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.0446311396, -0.7112978064}
Solution
y = {0.0446311396, -0.7112978064}