(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 = -4
-4 + -3u + u2 = -50 + 50

Combine like terms: -50 + 50 = 0
-4 + -3u + u2 = 0

Factor a trinomial.
(-1 + -1u)(4 + -1u) = 0

Subproblem 1
Set the factor '(-1 + -1u)' equal to zero and attempt to solve:

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 0

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

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

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

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

Divide each side by '-1'.
u = -1

Simplifying
u = -1
Subproblem 2
Set the factor '(4 + -1u)' equal to zero and attempt to solve:

Simplifying
4 + -1u = 0

Solving
4 + -1u = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1u = 0 + -4
-1u = 0 + -4

Combine like terms: 0 + -4 = -4
-1u = -4

Divide each side by '-1'.
u = 4

Simplifying
u = 4
Solution
u = {-1, 4}