(3u-2)(5+u)=0

Solution for (3u-2)(5+u)=0 equation:

Simplifying
(3u + -2)(5 + u) = 0

Reorder the terms:
(-2 + 3u)(5 + u) = 0

Multiply (-2 + 3u) * (5 + u)
(-2(5 + u) + 3u * (5 + u)) = 0
((5 * -2 + u * -2) + 3u * (5 + u)) = 0
((-10 + -2u) + 3u * (5 + u)) = 0
(-10 + -2u + (5 * 3u + u * 3u)) = 0
(-10 + -2u + (15u + 3u2)) = 0

Combine like terms: -2u + 15u = 13u
(-10 + 13u + 3u2) = 0

Solving
-10 + 13u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-5 + -1u)(2 + -3u) = 0

Subproblem 1
Set the factor '(-5 + -1u)' equal to zero and attempt to solve:

Simplifying
-5 + -1u = 0

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

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

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

Divide each side by '-1'.
u = -5

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

Simplifying
2 + -3u = 0

Solving
2 + -3u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3u = 0 + -2
-3u = 0 + -2

Combine like terms: 0 + -2 = -2
-3u = -2

Divide each side by '-3'.
u = 0.6666666667

Simplifying
u = 0.6666666667
Solution
u = {-5, 0.6666666667}