6(u-1)+5u+1=5(u+6)u

Solution for 6(u-1)+5u+1=5(u+6)u equation:

Simplifying
6(u + -1) + 5u + 1 = 5(u + 6) * u

Reorder the terms:
6(-1 + u) + 5u + 1 = 5(u + 6) * u
(-1 * 6 + u * 6) + 5u + 1 = 5(u + 6) * u
(-6 + 6u) + 5u + 1 = 5(u + 6) * u

Reorder the terms:
-6 + 1 + 6u + 5u = 5(u + 6) * u

Combine like terms: -6 + 1 = -5
-5 + 6u + 5u = 5(u + 6) * u

Combine like terms: 6u + 5u = 11u
-5 + 11u = 5(u + 6) * u

Reorder the terms:
-5 + 11u = 5(6 + u) * u

Reorder the terms for easier multiplication:
-5 + 11u = 5u(6 + u)
-5 + 11u = (6 * 5u + u * 5u)
-5 + 11u = (30u + 5u2)

Solving
-5 + 11u = 30u + 5u2

Solving for variable 'u'.

Combine like terms: 11u + -30u = -19u
-5 + -19u + -5u2 = 30u + 5u2 + -30u + -5u2

Reorder the terms:
-5 + -19u + -5u2 = 30u + -30u + 5u2 + -5u2

Combine like terms: 30u + -30u = 0
-5 + -19u + -5u2 = 0 + 5u2 + -5u2
-5 + -19u + -5u2 = 5u2 + -5u2

Combine like terms: 5u2 + -5u2 = 0
-5 + -19u + -5u2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 19u + 5u2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 19u + 5u2)' equal to zero and attempt to solve:

Simplifying
5 + 19u + 5u2 = 0

Solving
5 + 19u + 5u2 = 0

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

Divide each side by '5'.
1 + 3.8u + u2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 3.8u + -1 + u2 = 0 + -1

Reorder the terms:
1 + -1 + 3.8u + u2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3.8u + u2 = 0 + -1
3.8u + u2 = 0 + -1

Combine like terms: 0 + -1 = -1
3.8u + u2 = -1

The u term is 3.8u.  Take half its coefficient (1.9).
Square it (3.61) and add it to both sides.

Add '3.61' to each side of the equation.
3.8u + 3.61 + u2 = -1 + 3.61

Reorder the terms:
3.61 + 3.8u + u2 = -1 + 3.61

Combine like terms: -1 + 3.61 = 2.61
3.61 + 3.8u + u2 = 2.61

Factor a perfect square on the left side:
(u + 1.9)(u + 1.9) = 2.61

Calculate the square root of the right side: 1.615549442

Break this problem into two subproblems by setting 
(u + 1.9) equal to 1.615549442 and -1.615549442.

Subproblem 1
u + 1.9 = 1.615549442

Simplifying
u + 1.9 = 1.615549442

Reorder the terms:
1.9 + u = 1.615549442

Solving
1.9 + u = 1.615549442

Solving for variable 'u'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + u = 1.615549442 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + u = 1.615549442 + -1.9
u = 1.615549442 + -1.9

Combine like terms: 1.615549442 + -1.9 = -0.284450558
u = -0.284450558

Simplifying
u = -0.284450558

Subproblem 2
u + 1.9 = -1.615549442

Simplifying
u + 1.9 = -1.615549442

Reorder the terms:
1.9 + u = -1.615549442

Solving
1.9 + u = -1.615549442

Solving for variable 'u'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + u = -1.615549442 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + u = -1.615549442 + -1.9
u = -1.615549442 + -1.9

Combine like terms: -1.615549442 + -1.9 = -3.515549442
u = -3.515549442

Simplifying
u = -3.515549442

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-0.284450558, -3.515549442}
Solution
u = {-0.284450558, -3.515549442}