u+2(u+1)+1=6-u(3u-1)

Solution for u+2(u+1)+1=6-u(3u-1) equation:

Simplifying
u + 2(u + 1) + 1 = 6 + -1u(3u + -1)

Reorder the terms:
u + 2(1 + u) + 1 = 6 + -1u(3u + -1)
u + (1 * 2 + u * 2) + 1 = 6 + -1u(3u + -1)
u + (2 + 2u) + 1 = 6 + -1u(3u + -1)

Reorder the terms:
2 + 1 + u + 2u = 6 + -1u(3u + -1)

Combine like terms: 2 + 1 = 3
3 + u + 2u = 6 + -1u(3u + -1)

Combine like terms: u + 2u = 3u
3 + 3u = 6 + -1u(3u + -1)

Reorder the terms:
3 + 3u = 6 + -1u(-1 + 3u)
3 + 3u = 6 + (-1 * -1u + 3u * -1u)
3 + 3u = 6 + (1u + -3u2)

Solving
3 + 3u = 6 + 1u + -3u2

Solving for variable 'u'.

Reorder the terms:
3 + -6 + 3u + -1u + 3u2 = 6 + 1u + -3u2 + -6 + -1u + 3u2

Combine like terms: 3 + -6 = -3
-3 + 3u + -1u + 3u2 = 6 + 1u + -3u2 + -6 + -1u + 3u2

Combine like terms: 3u + -1u = 2u
-3 + 2u + 3u2 = 6 + 1u + -3u2 + -6 + -1u + 3u2

Reorder the terms:
-3 + 2u + 3u2 = 6 + -6 + 1u + -1u + -3u2 + 3u2

Combine like terms: 6 + -6 = 0
-3 + 2u + 3u2 = 0 + 1u + -1u + -3u2 + 3u2
-3 + 2u + 3u2 = 1u + -1u + -3u2 + 3u2

Combine like terms: 1u + -1u = 0
-3 + 2u + 3u2 = 0 + -3u2 + 3u2
-3 + 2u + 3u2 = -3u2 + 3u2

Combine like terms: -3u2 + 3u2 = 0
-3 + 2u + 3u2 = 0

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

Divide each side by '3'.
-1 + 0.6666666667u + u2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.6666666667u + 1 + u2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.6666666667u + u2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.6666666667u + u2 = 0 + 1
0.6666666667u + u2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.6666666667u + u2 = 1

The u term is 0.6666666667u.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667u + 0.1111111112 + u2 = 1 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667u + u2 = 1 + 0.1111111112

Combine like terms: 1 + 0.1111111112 = 1.1111111112
0.1111111112 + 0.6666666667u + u2 = 1.1111111112

Factor a perfect square on the left side:
(u + 0.3333333334)(u + 0.3333333334) = 1.1111111112

Calculate the square root of the right side: 1.054092553

Break this problem into two subproblems by setting 
(u + 0.3333333334) equal to 1.054092553 and -1.054092553.

Subproblem 1
u + 0.3333333334 = 1.054092553

Simplifying
u + 0.3333333334 = 1.054092553

Reorder the terms:
0.3333333334 + u = 1.054092553

Solving
0.3333333334 + u = 1.054092553

Solving for variable 'u'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + u = 1.054092553 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + u = 1.054092553 + -0.3333333334
u = 1.054092553 + -0.3333333334

Combine like terms: 1.054092553 + -0.3333333334 = 0.7207592196
u = 0.7207592196

Simplifying
u = 0.7207592196

Subproblem 2
u + 0.3333333334 = -1.054092553

Simplifying
u + 0.3333333334 = -1.054092553

Reorder the terms:
0.3333333334 + u = -1.054092553

Solving
0.3333333334 + u = -1.054092553

Solving for variable 'u'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + u = -1.054092553 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + u = -1.054092553 + -0.3333333334
u = -1.054092553 + -0.3333333334

Combine like terms: -1.054092553 + -0.3333333334 = -1.3874258864
u = -1.3874258864

Simplifying
u = -1.3874258864

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.7207592196, -1.3874258864}