y(y+6)=10

Solution for y(y+6)=10 equation:

Simplifying
y(y + 6) = 10

Reorder the terms:
y(6 + y) = 10
(6 * y + y * y) = 10
(6y + y2) = 10

Solving
6y + y2 = 10

Solving for variable 'y'.

Reorder the terms:
-10 + 6y + y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 6y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 6y + 10 + y2 = 0 + 10

Reorder the terms:
-10 + 10 + 6y + y2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 6y + y2 = 0 + 10
6y + y2 = 0 + 10

Combine like terms: 0 + 10 = 10
6y + y2 = 10

The y term is 6y.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6y + 9 + y2 = 10 + 9

Reorder the terms:
9 + 6y + y2 = 10 + 9

Combine like terms: 10 + 9 = 19
9 + 6y + y2 = 19

Factor a perfect square on the left side:
(y + 3)(y + 3) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(y + 3) equal to 4.358898944 and -4.358898944.

Subproblem 1
y + 3 = 4.358898944

Simplifying
y + 3 = 4.358898944

Reorder the terms:
3 + y = 4.358898944

Solving
3 + y = 4.358898944

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = 4.358898944 + -3

Combine like terms: 3 + -3 = 0
0 + y = 4.358898944 + -3
y = 4.358898944 + -3

Combine like terms: 4.358898944 + -3 = 1.358898944
y = 1.358898944

Simplifying
y = 1.358898944

Subproblem 2
y + 3 = -4.358898944

Simplifying
y + 3 = -4.358898944

Reorder the terms:
3 + y = -4.358898944

Solving
3 + y = -4.358898944

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = -4.358898944 + -3

Combine like terms: 3 + -3 = 0
0 + y = -4.358898944 + -3
y = -4.358898944 + -3

Combine like terms: -4.358898944 + -3 = -7.358898944
y = -7.358898944

Simplifying
y = -7.358898944

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.358898944, -7.358898944}