-2y(y-5)=y+1

Solution for -2y(y-5)=y+1 equation:

Simplifying
-2y(y + -5) = y + 1

Reorder the terms:
-2y(-5 + y) = y + 1
(-5 * -2y + y * -2y) = y + 1
(10y + -2y2) = y + 1

Reorder the terms:
10y + -2y2 = 1 + y

Solving
10y + -2y2 = 1 + y

Solving for variable 'y'.

Reorder the terms:
-1 + 10y + -1y + -2y2 = 1 + y + -1 + -1y

Combine like terms: 10y + -1y = 9y
-1 + 9y + -2y2 = 1 + y + -1 + -1y

Reorder the terms:
-1 + 9y + -2y2 = 1 + -1 + y + -1y

Combine like terms: 1 + -1 = 0
-1 + 9y + -2y2 = 0 + y + -1y
-1 + 9y + -2y2 = y + -1y

Combine like terms: y + -1y = 0
-1 + 9y + -2y2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
0.5 + -4.5y + y2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -4.5y + -0.5 + y2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -4.5y + y2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -4.5y + y2 = 0 + -0.5
-4.5y + y2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-4.5y + y2 = -0.5

The y term is -4.5y.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5y + 5.0625 + y2 = -0.5 + 5.0625

Reorder the terms:
5.0625 + -4.5y + y2 = -0.5 + 5.0625

Combine like terms: -0.5 + 5.0625 = 4.5625
5.0625 + -4.5y + y2 = 4.5625

Factor a perfect square on the left side:
(y + -2.25)(y + -2.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(y + -2.25) equal to 2.136000936 and -2.136000936.

Subproblem 1
y + -2.25 = 2.136000936

Simplifying
y + -2.25 = 2.136000936

Reorder the terms:
-2.25 + y = 2.136000936

Solving
-2.25 + y = 2.136000936

Solving for variable 'y'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + y = 2.136000936 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + y = 2.136000936 + 2.25
y = 2.136000936 + 2.25

Combine like terms: 2.136000936 + 2.25 = 4.386000936
y = 4.386000936

Simplifying
y = 4.386000936

Subproblem 2
y + -2.25 = -2.136000936

Simplifying
y + -2.25 = -2.136000936

Reorder the terms:
-2.25 + y = -2.136000936

Solving
-2.25 + y = -2.136000936

Solving for variable 'y'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + y = -2.136000936 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + y = -2.136000936 + 2.25
y = -2.136000936 + 2.25

Combine like terms: -2.136000936 + 2.25 = 0.113999064
y = 0.113999064

Simplifying
y = 0.113999064

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.386000936, 0.113999064}