y(y+6)=100

Solution for y(y+6)=100 equation:

Simplifying
y(y + 6) = 100

Reorder the terms:
y(6 + y) = 100
(6 * y + y * y) = 100
(6y + y2) = 100

Solving
6y + y2 = 100

Solving for variable 'y'.

Reorder the terms:
-100 + 6y + y2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 6y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 6y + 100 + y2 = 0 + 100

Reorder the terms:
-100 + 100 + 6y + y2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 6y + y2 = 0 + 100
6y + y2 = 0 + 100

Combine like terms: 0 + 100 = 100
6y + y2 = 100

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 = 100 + 9

Reorder the terms:
9 + 6y + y2 = 100 + 9

Combine like terms: 100 + 9 = 109
9 + 6y + y2 = 109

Factor a perfect square on the left side:
(y + 3)(y + 3) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(y + 3) equal to 10.440306509 and -10.440306509.

Subproblem 1
y + 3 = 10.440306509

Simplifying
y + 3 = 10.440306509

Reorder the terms:
3 + y = 10.440306509

Solving
3 + y = 10.440306509

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 = 10.440306509 + -3

Combine like terms: 3 + -3 = 0
0 + y = 10.440306509 + -3
y = 10.440306509 + -3

Combine like terms: 10.440306509 + -3 = 7.440306509
y = 7.440306509

Simplifying
y = 7.440306509

Subproblem 2
y + 3 = -10.440306509

Simplifying
y + 3 = -10.440306509

Reorder the terms:
3 + y = -10.440306509

Solving
3 + y = -10.440306509

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 = -10.440306509 + -3

Combine like terms: 3 + -3 = 0
0 + y = -10.440306509 + -3
y = -10.440306509 + -3

Combine like terms: -10.440306509 + -3 = -13.440306509
y = -13.440306509

Simplifying
y = -13.440306509

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.440306509, -13.440306509}