(u-9)(u+6)=50

Solution for (u-9)(u+6)=50 equation:

Simplifying
(u + -9)(u + 6) = 50

Reorder the terms:
(-9 + u)(u + 6) = 50

Reorder the terms:
(-9 + u)(6 + u) = 50

Multiply (-9 + u) * (6 + u)
(-9(6 + u) + u(6 + u)) = 50
((6 * -9 + u * -9) + u(6 + u)) = 50
((-54 + -9u) + u(6 + u)) = 50
(-54 + -9u + (6 * u + u * u)) = 50
(-54 + -9u + (6u + u2)) = 50

Combine like terms: -9u + 6u = -3u
(-54 + -3u + u2) = 50

Solving
-54 + -3u + u2 = 50

Solving for variable 'u'.

Reorder the terms:
-54 + -50 + -3u + u2 = 50 + -50

Combine like terms: -54 + -50 = -104
-104 + -3u + u2 = 50 + -50

Combine like terms: 50 + -50 = 0
-104 + -3u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '104' to each side of the equation.
-104 + -3u + 104 + u2 = 0 + 104

Reorder the terms:
-104 + 104 + -3u + u2 = 0 + 104

Combine like terms: -104 + 104 = 0
0 + -3u + u2 = 0 + 104
-3u + u2 = 0 + 104

Combine like terms: 0 + 104 = 104
-3u + u2 = 104

The u term is -3u.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3u + 2.25 + u2 = 104 + 2.25

Reorder the terms:
2.25 + -3u + u2 = 104 + 2.25

Combine like terms: 104 + 2.25 = 106.25
2.25 + -3u + u2 = 106.25

Factor a perfect square on the left side:
(u + -1.5)(u + -1.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(u + -1.5) equal to 10.307764064 and -10.307764064.

Subproblem 1
u + -1.5 = 10.307764064

Simplifying
u + -1.5 = 10.307764064

Reorder the terms:
-1.5 + u = 10.307764064

Solving
-1.5 + u = 10.307764064

Solving for variable 'u'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + u = 10.307764064 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = 10.307764064 + 1.5
u = 10.307764064 + 1.5

Combine like terms: 10.307764064 + 1.5 = 11.807764064
u = 11.807764064

Simplifying
u = 11.807764064

Subproblem 2
u + -1.5 = -10.307764064

Simplifying
u + -1.5 = -10.307764064

Reorder the terms:
-1.5 + u = -10.307764064

Solving
-1.5 + u = -10.307764064

Solving for variable 'u'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + u = -10.307764064 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = -10.307764064 + 1.5
u = -10.307764064 + 1.5

Combine like terms: -10.307764064 + 1.5 = -8.807764064
u = -8.807764064

Simplifying
u = -8.807764064

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {11.807764064, -8.807764064}