(9+u)(5u-1)=0

Solution for (9+u)(5u-1)=0 equation:

Simplifying
(9 + u)(5u + -1) = 0

Reorder the terms:
(9 + u)(-1 + 5u) = 0

Multiply (9 + u) * (-1 + 5u)
(9(-1 + 5u) + u(-1 + 5u)) = 0
((-1 * 9 + 5u * 9) + u(-1 + 5u)) = 0
((-9 + 45u) + u(-1 + 5u)) = 0
(-9 + 45u + (-1 * u + 5u * u)) = 0
(-9 + 45u + (-1u + 5u2)) = 0

Combine like terms: 45u + -1u = 44u
(-9 + 44u + 5u2) = 0

Solving
-9 + 44u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-9 + -1u)(1 + -5u) = 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 + -5u)' equal to zero and attempt to solve:

Simplifying
1 + -5u = 0

Solving
1 + -5u = 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 + -5u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5u = 0 + -1
-5u = 0 + -1

Combine like terms: 0 + -1 = -1
-5u = -1

Divide each side by '-5'.
u = 0.2

Simplifying
u = 0.2
Solution
u = {-9, 0.2}