y(y+4)-y=6

Solution for y(y+4)-y=6 equation:

Simplifying
y(y + 4) + -1y = 6

Reorder the terms:
y(4 + y) + -1y = 6
(4 * y + y * y) + -1y = 6
(4y + y2) + -1y = 6

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

Combine like terms: 4y + -1y = 3y
3y + y2 = 6

Solving
3y + y2 = 6

Solving for variable 'y'.

Reorder the terms:
-6 + 3y + y2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3y + 6 + y2 = 0 + 6

Reorder the terms:
-6 + 6 + 3y + y2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3y + y2 = 0 + 6
3y + y2 = 0 + 6

Combine like terms: 0 + 6 = 6
3y + y2 = 6

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 6 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + 3y + y2 = 8.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(y + 1.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
y + 1.5 = 2.872281323

Simplifying
y + 1.5 = 2.872281323

Reorder the terms:
1.5 + y = 2.872281323

Solving
1.5 + y = 2.872281323

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 2.872281323 + -1.5
y = 2.872281323 + -1.5

Combine like terms: 2.872281323 + -1.5 = 1.372281323
y = 1.372281323

Simplifying
y = 1.372281323

Subproblem 2
y + 1.5 = -2.872281323

Simplifying
y + 1.5 = -2.872281323

Reorder the terms:
1.5 + y = -2.872281323

Solving
1.5 + y = -2.872281323

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -2.872281323 + -1.5
y = -2.872281323 + -1.5

Combine like terms: -2.872281323 + -1.5 = -4.372281323
y = -4.372281323

Simplifying
y = -4.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.372281323, -4.372281323}