(8-u)(3u+2)=u

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Solution for (8-u)(3u+2)=u equation: 


Simplifying
(8 + -1u)(3u + 2) = u

Reorder the terms:
(8 + -1u)(2 + 3u) = u

Multiply (8 + -1u) * (2 + 3u)
(8(2 + 3u) + -1u * (2 + 3u)) = u
((2 * 8 + 3u * 8) + -1u * (2 + 3u)) = u
((16 + 24u) + -1u * (2 + 3u)) = u
(16 + 24u + (2 * -1u + 3u * -1u)) = u
(16 + 24u + (-2u + -3u2)) = u

Combine like terms: 24u + -2u = 22u
(16 + 22u + -3u2) = u

Solving
16 + 22u + -3u2 = u

Solving for variable 'u'.

Reorder the terms:
16 + 22u + -1u + -3u2 = u + -1u

Combine like terms: 22u + -1u = 21u
16 + 21u + -3u2 = u + -1u

Combine like terms: u + -1u = 0
16 + 21u + -3u2 = 0

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

Divide each side by '-3'.
-5.333333333 + -7u + u2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -7u + 5.333333333 + u2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -7u + u2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -7u + u2 = 0 + 5.333333333
-7u + u2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-7u + u2 = 5.333333333

The u term is -7u.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7u + 12.25 + u2 = 5.333333333 + 12.25

Reorder the terms:
12.25 + -7u + u2 = 5.333333333 + 12.25

Combine like terms: 5.333333333 + 12.25 = 17.583333333
12.25 + -7u + u2 = 17.583333333

Factor a perfect square on the left side:
(u + -3.5)(u + -3.5) = 17.583333333

Calculate the square root of the right side: 4.193248542

Break this problem into two subproblems by setting 
(u + -3.5) equal to 4.193248542 and -4.193248542.


Subproblem 1
u + -3.5 = 4.193248542

Simplifying
u + -3.5 = 4.193248542

Reorder the terms:
-3.5 + u = 4.193248542

Solving
-3.5 + u = 4.193248542

Solving for variable 'u'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + u = 4.193248542 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + u = 4.193248542 + 3.5
u = 4.193248542 + 3.5

Combine like terms: 4.193248542 + 3.5 = 7.693248542
u = 7.693248542

Simplifying
u = 7.693248542


Subproblem 2
u + -3.5 = -4.193248542

Simplifying
u + -3.5 = -4.193248542

Reorder the terms:
-3.5 + u = -4.193248542

Solving
-3.5 + u = -4.193248542

Solving for variable 'u'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + u = -4.193248542 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + u = -4.193248542 + 3.5
u = -4.193248542 + 3.5

Combine like terms: -4.193248542 + 3.5 = -0.693248542
u = -0.693248542

Simplifying
u = -0.693248542


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {7.693248542, -0.693248542}

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