(3u-5)(4+u)=0

Solution for (3u-5)(4+u)=0 equation:

Simplifying
(3u + -5)(4 + u) = 0

Reorder the terms:
(-5 + 3u)(4 + u) = 0

Multiply (-5 + 3u) * (4 + u)
(-5(4 + u) + 3u * (4 + u)) = 0
((4 * -5 + u * -5) + 3u * (4 + u)) = 0
((-20 + -5u) + 3u * (4 + u)) = 0
(-20 + -5u + (4 * 3u + u * 3u)) = 0
(-20 + -5u + (12u + 3u2)) = 0

Combine like terms: -5u + 12u = 7u
(-20 + 7u + 3u2) = 0

Solving
-20 + 7u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-4 + -1u)(5 + -3u) = 0

Subproblem 1
Set the factor '(-4 + -1u)' equal to zero and attempt to solve:

Simplifying
-4 + -1u = 0

Solving
-4 + -1u = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1u = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1u = 0 + 4
-1u = 0 + 4

Combine like terms: 0 + 4 = 4
-1u = 4

Divide each side by '-1'.
u = -4

Simplifying
u = -4
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 = {-4, 1.666666667}