6=u(u+2)

Solution for 6=u(u+2) equation:

Simplifying
6 = u(u + 2)

Reorder the terms:
6 = u(2 + u)
6 = (2 * u + u * u)
6 = (2u + u2)

Solving
6 = 2u + u2

Solving for variable 'u'.

Reorder the terms:
6 + -2u + -1u2 = 2u + -2u + u2 + -1u2

Combine like terms: 2u + -2u = 0
6 + -2u + -1u2 = 0 + u2 + -1u2
6 + -2u + -1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
6 + -2u + -1u2 = 0

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

Divide each side by '-1'.
-6 + 2u + u2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 2u + 6 + u2 = 0 + 6

Reorder the terms:
-6 + 6 + 2u + u2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2u + u2 = 0 + 6
2u + u2 = 0 + 6

Combine like terms: 0 + 6 = 6
2u + u2 = 6

The u term is 2u.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2u + 1 + u2 = 6 + 1

Reorder the terms:
1 + 2u + u2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + 2u + u2 = 7

Factor a perfect square on the left side:
(u + 1)(u + 1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(u + 1) equal to 2.645751311 and -2.645751311.

Subproblem 1
u + 1 = 2.645751311

Simplifying
u + 1 = 2.645751311

Reorder the terms:
1 + u = 2.645751311

Solving
1 + u = 2.645751311

Solving for variable 'u'.

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

Add '-1' to each side of the equation.
1 + -1 + u = 2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + u = 2.645751311 + -1
u = 2.645751311 + -1

Combine like terms: 2.645751311 + -1 = 1.645751311
u = 1.645751311

Simplifying
u = 1.645751311

Subproblem 2
u + 1 = -2.645751311

Simplifying
u + 1 = -2.645751311

Reorder the terms:
1 + u = -2.645751311

Solving
1 + u = -2.645751311

Solving for variable 'u'.

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

Add '-1' to each side of the equation.
1 + -1 + u = -2.645751311 + -1

Combine like terms: 1 + -1 = 0
0 + u = -2.645751311 + -1
u = -2.645751311 + -1

Combine like terms: -2.645751311 + -1 = -3.645751311
u = -3.645751311

Simplifying
u = -3.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.645751311, -3.645751311}