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

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

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

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

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

Combine like terms: 9u + -5u = 4u
(-15 + 4u + 3u2) = 0

Solving
-15 + 4u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3 + -1u)(5 + -3u) = 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 '(5 + -3u)' equal to zero and attempt to solve:

Simplifying
5 + -3u = 0

Solving
5 + -3u = 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 + -3u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3u = 0 + -5
-3u = 0 + -5

Combine like terms: 0 + -5 = -5
-3u = -5

Divide each side by '-3'.
u = 1.666666667

Simplifying
u = 1.666666667
Solution
u = {-3, 1.666666667}