(9+u)(4u-5)=0

Solution for (9+u)(4u-5)=0 equation:

Simplifying
(9 + u)(4u + -5) = 0

Reorder the terms:
(9 + u)(-5 + 4u) = 0

Multiply (9 + u) * (-5 + 4u)
(9(-5 + 4u) + u(-5 + 4u)) = 0
((-5 * 9 + 4u * 9) + u(-5 + 4u)) = 0
((-45 + 36u) + u(-5 + 4u)) = 0
(-45 + 36u + (-5 * u + 4u * u)) = 0
(-45 + 36u + (-5u + 4u2)) = 0

Combine like terms: 36u + -5u = 31u
(-45 + 31u + 4u2) = 0

Solving
-45 + 31u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-9 + -1u)(5 + -4u) = 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 '(5 + -4u)' equal to zero and attempt to solve:

Simplifying
5 + -4u = 0

Solving
5 + -4u = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4u = 0 + -5
-4u = 0 + -5

Combine like terms: 0 + -5 = -5
-4u = -5

Divide each side by '-4'.
u = 1.25

Simplifying
u = 1.25
Solution
u = {-9, 1.25}