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

Solution for (8+u)(5u-3)=0 equation:

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

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

Multiply (8 + u) * (-3 + 5u)
(8(-3 + 5u) + u(-3 + 5u)) = 0
((-3 * 8 + 5u * 8) + u(-3 + 5u)) = 0
((-24 + 40u) + u(-3 + 5u)) = 0
(-24 + 40u + (-3 * u + 5u * u)) = 0
(-24 + 40u + (-3u + 5u2)) = 0

Combine like terms: 40u + -3u = 37u
(-24 + 37u + 5u2) = 0

Solving
-24 + 37u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-8 + -1u)(3 + -5u) = 0

Subproblem 1
Set the factor '(-8 + -1u)' equal to zero and attempt to solve:

Simplifying
-8 + -1u = 0

Solving
-8 + -1u = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1u = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1u = 0 + 8
-1u = 0 + 8

Combine like terms: 0 + 8 = 8
-1u = 8

Divide each side by '-1'.
u = -8

Simplifying
u = -8
Subproblem 2
Set the factor '(3 + -5u)' equal to zero and attempt to solve:

Simplifying
3 + -5u = 0

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

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

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

Divide each side by '-5'.
u = 0.6

Simplifying
u = 0.6
Solution
u = {-8, 0.6}