(5y+11)=(12y+-10)30y+13

Solution for (5y+11)=(12y+-10)30y+13 equation:

Simplifying
(5y + 11) = (12y + -10) * 30y + 13

Reorder the terms:
(11 + 5y) = (12y + -10) * 30y + 13

Remove parenthesis around (11 + 5y)
11 + 5y = (12y + -10) * 30y + 13

Reorder the terms:
11 + 5y = (-10 + 12y) * 30y + 13

Reorder the terms for easier multiplication:
11 + 5y = 30y(-10 + 12y) + 13
11 + 5y = (-10 * 30y + 12y * 30y) + 13
11 + 5y = (-300y + 360y2) + 13

Reorder the terms:
11 + 5y = 13 + -300y + 360y2

Solving
11 + 5y = 13 + -300y + 360y2

Solving for variable 'y'.

Reorder the terms:
11 + -13 + 5y + 300y + -360y2 = 13 + -300y + 360y2 + -13 + 300y + -360y2

Combine like terms: 11 + -13 = -2
-2 + 5y + 300y + -360y2 = 13 + -300y + 360y2 + -13 + 300y + -360y2

Combine like terms: 5y + 300y = 305y
-2 + 305y + -360y2 = 13 + -300y + 360y2 + -13 + 300y + -360y2

Reorder the terms:
-2 + 305y + -360y2 = 13 + -13 + -300y + 300y + 360y2 + -360y2

Combine like terms: 13 + -13 = 0
-2 + 305y + -360y2 = 0 + -300y + 300y + 360y2 + -360y2
-2 + 305y + -360y2 = -300y + 300y + 360y2 + -360y2

Combine like terms: -300y + 300y = 0
-2 + 305y + -360y2 = 0 + 360y2 + -360y2
-2 + 305y + -360y2 = 360y2 + -360y2

Combine like terms: 360y2 + -360y2 = 0
-2 + 305y + -360y2 = 0

Begin completing the square.  Divide all terms by
-360 the coefficient of the squared term: 

Divide each side by '-360'.
0.005555555556 + -0.8472222222y + y2 = 0

Move the constant term to the right:

Add '-0.005555555556' to each side of the equation.
0.005555555556 + -0.8472222222y + -0.005555555556 + y2 = 0 + -0.005555555556

Reorder the terms:
0.005555555556 + -0.005555555556 + -0.8472222222y + y2 = 0 + -0.005555555556

Combine like terms: 0.005555555556 + -0.005555555556 = 0.000000000000
0.000000000000 + -0.8472222222y + y2 = 0 + -0.005555555556
-0.8472222222y + y2 = 0 + -0.005555555556

Combine like terms: 0 + -0.005555555556 = -0.005555555556
-0.8472222222y + y2 = -0.005555555556

The y term is -0.8472222222y.  Take half its coefficient (-0.4236111111).
Square it (0.1794463734) and add it to both sides.

Add '0.1794463734' to each side of the equation.
-0.8472222222y + 0.1794463734 + y2 = -0.005555555556 + 0.1794463734

Reorder the terms:
0.1794463734 + -0.8472222222y + y2 = -0.005555555556 + 0.1794463734

Combine like terms: -0.005555555556 + 0.1794463734 = 0.173890817844
0.1794463734 + -0.8472222222y + y2 = 0.173890817844

Factor a perfect square on the left side:
(y + -0.4236111111)(y + -0.4236111111) = 0.173890817844

Calculate the square root of the right side: 0.41700218

Break this problem into two subproblems by setting 
(y + -0.4236111111) equal to 0.41700218 and -0.41700218.

Subproblem 1
y + -0.4236111111 = 0.41700218

Simplifying
y + -0.4236111111 = 0.41700218

Reorder the terms:
-0.4236111111 + y = 0.41700218

Solving
-0.4236111111 + y = 0.41700218

Solving for variable 'y'.

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

Add '0.4236111111' to each side of the equation.
-0.4236111111 + 0.4236111111 + y = 0.41700218 + 0.4236111111

Combine like terms: -0.4236111111 + 0.4236111111 = 0.0000000000
0.0000000000 + y = 0.41700218 + 0.4236111111
y = 0.41700218 + 0.4236111111

Combine like terms: 0.41700218 + 0.4236111111 = 0.8406132911
y = 0.8406132911

Simplifying
y = 0.8406132911

Subproblem 2
y + -0.4236111111 = -0.41700218

Simplifying
y + -0.4236111111 = -0.41700218

Reorder the terms:
-0.4236111111 + y = -0.41700218

Solving
-0.4236111111 + y = -0.41700218

Solving for variable 'y'.

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

Add '0.4236111111' to each side of the equation.
-0.4236111111 + 0.4236111111 + y = -0.41700218 + 0.4236111111

Combine like terms: -0.4236111111 + 0.4236111111 = 0.0000000000
0.0000000000 + y = -0.41700218 + 0.4236111111
y = -0.41700218 + 0.4236111111

Combine like terms: -0.41700218 + 0.4236111111 = 0.0066089311
y = 0.0066089311

Simplifying
y = 0.0066089311

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.8406132911, 0.0066089311}