6+y-10y=y^2+5y

Solution for 6+y-10y=y^2+5y equation:

Simplifying
6 + y + -10y = y2 + 5y

Combine like terms: y + -10y = -9y
6 + -9y = y2 + 5y

Reorder the terms:
6 + -9y = 5y + y2

Solving
6 + -9y = 5y + y2

Solving for variable 'y'.

Combine like terms: -9y + -5y = -14y
6 + -14y + -1y2 = 5y + y2 + -5y + -1y2

Reorder the terms:
6 + -14y + -1y2 = 5y + -5y + y2 + -1y2

Combine like terms: 5y + -5y = 0
6 + -14y + -1y2 = 0 + y2 + -1y2
6 + -14y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6 + -14y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 14y + y2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 14y + 6 + y2 = 0 + 6

Reorder the terms:
-6 + 6 + 14y + y2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 14y + y2 = 0 + 6
14y + y2 = 0 + 6

Combine like terms: 0 + 6 = 6
14y + y2 = 6

The y term is 14y.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14y + 49 + y2 = 6 + 49

Reorder the terms:
49 + 14y + y2 = 6 + 49

Combine like terms: 6 + 49 = 55
49 + 14y + y2 = 55

Factor a perfect square on the left side:
(y + 7)(y + 7) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(y + 7) equal to 7.416198487 and -7.416198487.

Subproblem 1
y + 7 = 7.416198487

Simplifying
y + 7 = 7.416198487

Reorder the terms:
7 + y = 7.416198487

Solving
7 + y = 7.416198487

Solving for variable 'y'.

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

Add '-7' to each side of the equation.
7 + -7 + y = 7.416198487 + -7

Combine like terms: 7 + -7 = 0
0 + y = 7.416198487 + -7
y = 7.416198487 + -7

Combine like terms: 7.416198487 + -7 = 0.416198487
y = 0.416198487

Simplifying
y = 0.416198487

Subproblem 2
y + 7 = -7.416198487

Simplifying
y + 7 = -7.416198487

Reorder the terms:
7 + y = -7.416198487

Solving
7 + y = -7.416198487

Solving for variable 'y'.

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

Add '-7' to each side of the equation.
7 + -7 + y = -7.416198487 + -7

Combine like terms: 7 + -7 = 0
0 + y = -7.416198487 + -7
y = -7.416198487 + -7

Combine like terms: -7.416198487 + -7 = -14.416198487
y = -14.416198487

Simplifying
y = -14.416198487

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.416198487, -14.416198487}