(3u-8)(4+u)=0

Solution for (3u-8)(4+u)=0 equation:

Simplifying
(3u + -8)(4 + u) = 0

Reorder the terms:
(-8 + 3u)(4 + u) = 0

Multiply (-8 + 3u) * (4 + u)
(-8(4 + u) + 3u * (4 + u)) = 0
((4 * -8 + u * -8) + 3u * (4 + u)) = 0
((-32 + -8u) + 3u * (4 + u)) = 0
(-32 + -8u + (4 * 3u + u * 3u)) = 0
(-32 + -8u + (12u + 3u2)) = 0

Combine like terms: -8u + 12u = 4u
(-32 + 4u + 3u2) = 0

Solving
-32 + 4u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-4 + -1u)(8 + -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 '(8 + -3u)' equal to zero and attempt to solve:

Simplifying
8 + -3u = 0

Solving
8 + -3u = 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 + -3u = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3u = 0 + -8
-3u = 0 + -8

Combine like terms: 0 + -8 = -8
-3u = -8

Divide each side by '-3'.
u = 2.666666667

Simplifying
u = 2.666666667
Solution
u = {-4, 2.666666667}