11(4-6y)5(13y+1)=9

Solution for 11(4-6y)5(13y+1)=9 equation:

Simplifying
11(4 + -6y) * 5(13y + 1) = 9

Reorder the terms:
11(4 + -6y) * 5(1 + 13y) = 9

Reorder the terms for easier multiplication:
11 * 5(4 + -6y)(1 + 13y) = 9

Multiply 11 * 5
55(4 + -6y)(1 + 13y) = 9

Multiply (4 + -6y) * (1 + 13y)
55(4(1 + 13y) + -6y * (1 + 13y)) = 9
55((1 * 4 + 13y * 4) + -6y * (1 + 13y)) = 9
55((4 + 52y) + -6y * (1 + 13y)) = 9
55(4 + 52y + (1 * -6y + 13y * -6y)) = 9
55(4 + 52y + (-6y + -78y2)) = 9

Combine like terms: 52y + -6y = 46y
55(4 + 46y + -78y2) = 9
(4 * 55 + 46y * 55 + -78y2 * 55) = 9
(220 + 2530y + -4290y2) = 9

Solving
220 + 2530y + -4290y2 = 9

Solving for variable 'y'.

Reorder the terms:
220 + -9 + 2530y + -4290y2 = 9 + -9

Combine like terms: 220 + -9 = 211
211 + 2530y + -4290y2 = 9 + -9

Combine like terms: 9 + -9 = 0
211 + 2530y + -4290y2 = 0

Begin completing the square.  Divide all terms by
-4290 the coefficient of the squared term: 

Divide each side by '-4290'.
-0.04918414918 + -0.5897435897y + y2 = 0.0

Move the constant term to the right:

Add '0.04918414918' to each side of the equation.
-0.04918414918 + -0.5897435897y + 0.04918414918 + y2 = 0.0 + 0.04918414918

Reorder the terms:
-0.04918414918 + 0.04918414918 + -0.5897435897y + y2 = 0.0 + 0.04918414918

Combine like terms: -0.04918414918 + 0.04918414918 = 0.00000000000
0.00000000000 + -0.5897435897y + y2 = 0.0 + 0.04918414918
-0.5897435897y + y2 = 0.0 + 0.04918414918

Combine like terms: 0.0 + 0.04918414918 = 0.04918414918
-0.5897435897y + y2 = 0.04918414918

The y term is -0.5897435897y.  Take half its coefficient (-0.2948717949).
Square it (0.08694937543) and add it to both sides.

Add '0.08694937543' to each side of the equation.
-0.5897435897y + 0.08694937543 + y2 = 0.04918414918 + 0.08694937543

Reorder the terms:
0.08694937543 + -0.5897435897y + y2 = 0.04918414918 + 0.08694937543

Combine like terms: 0.04918414918 + 0.08694937543 = 0.13613352461
0.08694937543 + -0.5897435897y + y2 = 0.13613352461

Factor a perfect square on the left side:
(y + -0.2948717949)(y + -0.2948717949) = 0.13613352461

Calculate the square root of the right side: 0.368962769

Break this problem into two subproblems by setting 
(y + -0.2948717949) equal to 0.368962769 and -0.368962769.

Subproblem 1
y + -0.2948717949 = 0.368962769

Simplifying
y + -0.2948717949 = 0.368962769

Reorder the terms:
-0.2948717949 + y = 0.368962769

Solving
-0.2948717949 + y = 0.368962769

Solving for variable 'y'.

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

Add '0.2948717949' to each side of the equation.
-0.2948717949 + 0.2948717949 + y = 0.368962769 + 0.2948717949

Combine like terms: -0.2948717949 + 0.2948717949 = 0.0000000000
0.0000000000 + y = 0.368962769 + 0.2948717949
y = 0.368962769 + 0.2948717949

Combine like terms: 0.368962769 + 0.2948717949 = 0.6638345639
y = 0.6638345639

Simplifying
y = 0.6638345639

Subproblem 2
y + -0.2948717949 = -0.368962769

Simplifying
y + -0.2948717949 = -0.368962769

Reorder the terms:
-0.2948717949 + y = -0.368962769

Solving
-0.2948717949 + y = -0.368962769

Solving for variable 'y'.

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

Add '0.2948717949' to each side of the equation.
-0.2948717949 + 0.2948717949 + y = -0.368962769 + 0.2948717949

Combine like terms: -0.2948717949 + 0.2948717949 = 0.0000000000
0.0000000000 + y = -0.368962769 + 0.2948717949
y = -0.368962769 + 0.2948717949

Combine like terms: -0.368962769 + 0.2948717949 = -0.0740909741
y = -0.0740909741

Simplifying
y = -0.0740909741

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.6638345639, -0.0740909741}