(9+u)(2u-1)=0

Solution for (9+u)(2u-1)=0 equation:

Simplifying
(9 + u)(2u + -1) = 0

Reorder the terms:
(9 + u)(-1 + 2u) = 0

Multiply (9 + u) * (-1 + 2u)
(9(-1 + 2u) + u(-1 + 2u)) = 0
((-1 * 9 + 2u * 9) + u(-1 + 2u)) = 0
((-9 + 18u) + u(-1 + 2u)) = 0
(-9 + 18u + (-1 * u + 2u * u)) = 0
(-9 + 18u + (-1u + 2u2)) = 0

Combine like terms: 18u + -1u = 17u
(-9 + 17u + 2u2) = 0

Solving
-9 + 17u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-9 + -1u)(1 + -2u) = 0

Subproblem 1
Set the factor '(-9 + -1u)' equal to zero and attempt to solve:

Simplifying
-9 + -1u = 0

Solving
-9 + -1u = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1u = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1u = 0 + 9
-1u = 0 + 9

Combine like terms: 0 + 9 = 9
-1u = 9

Divide each side by '-1'.
u = -9

Simplifying
u = -9
Subproblem 2
Set the factor '(1 + -2u)' equal to zero and attempt to solve:

Simplifying
1 + -2u = 0

Solving
1 + -2u = 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 + -2u = 0 + -1

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

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

Divide each side by '-2'.
u = 0.5

Simplifying
u = 0.5
Solution
u = {-9, 0.5}