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

Solution for (3+u)(5u-9)=0 equation:

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

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

Multiply (3 + u) * (-9 + 5u)
(3(-9 + 5u) + u(-9 + 5u)) = 0
((-9 * 3 + 5u * 3) + u(-9 + 5u)) = 0
((-27 + 15u) + u(-9 + 5u)) = 0
(-27 + 15u + (-9 * u + 5u * u)) = 0
(-27 + 15u + (-9u + 5u2)) = 0

Combine like terms: 15u + -9u = 6u
(-27 + 6u + 5u2) = 0

Solving
-27 + 6u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3 + -1u)(9 + -5u) = 0

Subproblem 1
Set the factor '(-3 + -1u)' equal to zero and attempt to solve:

Simplifying
-3 + -1u = 0

Solving
-3 + -1u = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1u = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1u = 0 + 3
-1u = 0 + 3

Combine like terms: 0 + 3 = 3
-1u = 3

Divide each side by '-1'.
u = -3

Simplifying
u = -3
Subproblem 2
Set the factor '(9 + -5u)' equal to zero and attempt to solve:

Simplifying
9 + -5u = 0

Solving
9 + -5u = 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 + -5u = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5u = 0 + -9
-5u = 0 + -9

Combine like terms: 0 + -9 = -9
-5u = -9

Divide each side by '-5'.
u = 1.8

Simplifying
u = 1.8
Solution
u = {-3, 1.8}