(y+2)(y+5)=(2y-1)(y+6)

Solution for (y+2)(y+5)=(2y-1)(y+6) equation:

Simplifying
(y + 2)(y + 5) = (2y + -1)(y + 6)

Reorder the terms:
(2 + y)(y + 5) = (2y + -1)(y + 6)

Reorder the terms:
(2 + y)(5 + y) = (2y + -1)(y + 6)

Multiply (2 + y) * (5 + y)
(2(5 + y) + y(5 + y)) = (2y + -1)(y + 6)
((5 * 2 + y * 2) + y(5 + y)) = (2y + -1)(y + 6)
((10 + 2y) + y(5 + y)) = (2y + -1)(y + 6)
(10 + 2y + (5 * y + y * y)) = (2y + -1)(y + 6)
(10 + 2y + (5y + y2)) = (2y + -1)(y + 6)

Combine like terms: 2y + 5y = 7y
(10 + 7y + y2) = (2y + -1)(y + 6)

Reorder the terms:
10 + 7y + y2 = (-1 + 2y)(y + 6)

Reorder the terms:
10 + 7y + y2 = (-1 + 2y)(6 + y)

Multiply (-1 + 2y) * (6 + y)
10 + 7y + y2 = (-1(6 + y) + 2y * (6 + y))
10 + 7y + y2 = ((6 * -1 + y * -1) + 2y * (6 + y))
10 + 7y + y2 = ((-6 + -1y) + 2y * (6 + y))
10 + 7y + y2 = (-6 + -1y + (6 * 2y + y * 2y))
10 + 7y + y2 = (-6 + -1y + (12y + 2y2))

Combine like terms: -1y + 12y = 11y
10 + 7y + y2 = (-6 + 11y + 2y2)

Solving
10 + 7y + y2 = -6 + 11y + 2y2

Solving for variable 'y'.

Reorder the terms:
10 + 6 + 7y + -11y + y2 + -2y2 = -6 + 11y + 2y2 + 6 + -11y + -2y2

Combine like terms: 10 + 6 = 16
16 + 7y + -11y + y2 + -2y2 = -6 + 11y + 2y2 + 6 + -11y + -2y2

Combine like terms: 7y + -11y = -4y
16 + -4y + y2 + -2y2 = -6 + 11y + 2y2 + 6 + -11y + -2y2

Combine like terms: y2 + -2y2 = -1y2
16 + -4y + -1y2 = -6 + 11y + 2y2 + 6 + -11y + -2y2

Reorder the terms:
16 + -4y + -1y2 = -6 + 6 + 11y + -11y + 2y2 + -2y2

Combine like terms: -6 + 6 = 0
16 + -4y + -1y2 = 0 + 11y + -11y + 2y2 + -2y2
16 + -4y + -1y2 = 11y + -11y + 2y2 + -2y2

Combine like terms: 11y + -11y = 0
16 + -4y + -1y2 = 0 + 2y2 + -2y2
16 + -4y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
16 + -4y + -1y2 = 0

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

Divide each side by '-1'.
-16 + 4y + y2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 4y + 16 + y2 = 0 + 16

Reorder the terms:
-16 + 16 + 4y + y2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 4y + y2 = 0 + 16
4y + y2 = 0 + 16

Combine like terms: 0 + 16 = 16
4y + y2 = 16

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 16 + 4

Reorder the terms:
4 + 4y + y2 = 16 + 4

Combine like terms: 16 + 4 = 20
4 + 4y + y2 = 20

Factor a perfect square on the left side:
(y + 2)(y + 2) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(y + 2) equal to 4.472135955 and -4.472135955.

Subproblem 1
y + 2 = 4.472135955

Simplifying
y + 2 = 4.472135955

Reorder the terms:
2 + y = 4.472135955

Solving
2 + y = 4.472135955

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = 4.472135955 + -2

Combine like terms: 2 + -2 = 0
0 + y = 4.472135955 + -2
y = 4.472135955 + -2

Combine like terms: 4.472135955 + -2 = 2.472135955
y = 2.472135955

Simplifying
y = 2.472135955

Subproblem 2
y + 2 = -4.472135955

Simplifying
y + 2 = -4.472135955

Reorder the terms:
2 + y = -4.472135955

Solving
2 + y = -4.472135955

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = -4.472135955 + -2

Combine like terms: 2 + -2 = 0
0 + y = -4.472135955 + -2
y = -4.472135955 + -2

Combine like terms: -4.472135955 + -2 = -6.472135955
y = -6.472135955

Simplifying
y = -6.472135955

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.472135955, -6.472135955}