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

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

Simplifying
(5 + -1u)(4u + 3) = 0

Reorder the terms:
(5 + -1u)(3 + 4u) = 0

Multiply (5 + -1u) * (3 + 4u)
(5(3 + 4u) + -1u * (3 + 4u)) = 0
((3 * 5 + 4u * 5) + -1u * (3 + 4u)) = 0
((15 + 20u) + -1u * (3 + 4u)) = 0
(15 + 20u + (3 * -1u + 4u * -1u)) = 0
(15 + 20u + (-3u + -4u2)) = 0

Combine like terms: 20u + -3u = 17u
(15 + 17u + -4u2) = 0

Solving
15 + 17u + -4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(5 + -1u)(3 + 4u) = 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 '(3 + 4u)' equal to zero and attempt to solve:

Simplifying
3 + 4u = 0

Solving
3 + 4u = 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 + 4u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4u = 0 + -3
4u = 0 + -3

Combine like terms: 0 + -3 = -3
4u = -3

Divide each side by '4'.
u = -0.75

Simplifying
u = -0.75
Solution
u = {5, -0.75}