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

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

Simplifying
y2 + 5y = ((y + 5) + -2)(5y + 1)

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

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

Remove parenthesis around (5 + y)
5y + y2 = (5 + y + -2)(5y + 1)

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

Combine like terms: 5 + -2 = 3
5y + y2 = (3 + y)(5y + 1)

Reorder the terms:
5y + y2 = (3 + y)(1 + 5y)

Multiply (3 + y) * (1 + 5y)
5y + y2 = (3(1 + 5y) + y(1 + 5y))
5y + y2 = ((1 * 3 + 5y * 3) + y(1 + 5y))
5y + y2 = ((3 + 15y) + y(1 + 5y))
5y + y2 = (3 + 15y + (1 * y + 5y * y))
5y + y2 = (3 + 15y + (1y + 5y2))

Combine like terms: 15y + 1y = 16y
5y + y2 = (3 + 16y + 5y2)

Solving
5y + y2 = 3 + 16y + 5y2

Solving for variable 'y'.

Reorder the terms:
-3 + 5y + -16y + y2 + -5y2 = 3 + 16y + 5y2 + -3 + -16y + -5y2

Combine like terms: 5y + -16y = -11y
-3 + -11y + y2 + -5y2 = 3 + 16y + 5y2 + -3 + -16y + -5y2

Combine like terms: y2 + -5y2 = -4y2
-3 + -11y + -4y2 = 3 + 16y + 5y2 + -3 + -16y + -5y2

Reorder the terms:
-3 + -11y + -4y2 = 3 + -3 + 16y + -16y + 5y2 + -5y2

Combine like terms: 3 + -3 = 0
-3 + -11y + -4y2 = 0 + 16y + -16y + 5y2 + -5y2
-3 + -11y + -4y2 = 16y + -16y + 5y2 + -5y2

Combine like terms: 16y + -16y = 0
-3 + -11y + -4y2 = 0 + 5y2 + -5y2
-3 + -11y + -4y2 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
-3 + -11y + -4y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 11y + 4y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 11y + 4y2)' equal to zero and attempt to solve:

Simplifying
3 + 11y + 4y2 = 0

Solving
3 + 11y + 4y2 = 0

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

Divide each side by '4'.
0.75 + 2.75y + y2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 2.75y + -0.75 + y2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 2.75y + y2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 2.75y + y2 = 0 + -0.75
2.75y + y2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
2.75y + y2 = -0.75

The y term is 2.75y.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75y + 1.890625 + y2 = -0.75 + 1.890625

Reorder the terms:
1.890625 + 2.75y + y2 = -0.75 + 1.890625

Combine like terms: -0.75 + 1.890625 = 1.140625
1.890625 + 2.75y + y2 = 1.140625

Factor a perfect square on the left side:
(y + 1.375)(y + 1.375) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(y + 1.375) equal to 1.068000468 and -1.068000468.

Subproblem 1
y + 1.375 = 1.068000468

Simplifying
y + 1.375 = 1.068000468

Reorder the terms:
1.375 + y = 1.068000468

Solving
1.375 + y = 1.068000468

Solving for variable 'y'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + y = 1.068000468 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + y = 1.068000468 + -1.375
y = 1.068000468 + -1.375

Combine like terms: 1.068000468 + -1.375 = -0.306999532
y = -0.306999532

Simplifying
y = -0.306999532

Subproblem 2
y + 1.375 = -1.068000468

Simplifying
y + 1.375 = -1.068000468

Reorder the terms:
1.375 + y = -1.068000468

Solving
1.375 + y = -1.068000468

Solving for variable 'y'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + y = -1.068000468 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + y = -1.068000468 + -1.375
y = -1.068000468 + -1.375

Combine like terms: -1.068000468 + -1.375 = -2.443000468
y = -2.443000468

Simplifying
y = -2.443000468

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.306999532, -2.443000468}
Solution
y = {-0.306999532, -2.443000468}