(3u-8)(6+u)=0

Solution for (3u-8)(6+u)=0 equation:

Simplifying
(3u + -8)(6 + u) = 0

Reorder the terms:
(-8 + 3u)(6 + u) = 0

Multiply (-8 + 3u) * (6 + u)
(-8(6 + u) + 3u * (6 + u)) = 0
((6 * -8 + u * -8) + 3u * (6 + u)) = 0
((-48 + -8u) + 3u * (6 + u)) = 0
(-48 + -8u + (6 * 3u + u * 3u)) = 0
(-48 + -8u + (18u + 3u2)) = 0

Combine like terms: -8u + 18u = 10u
(-48 + 10u + 3u2) = 0

Solving
-48 + 10u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + -1u)(8 + -3u) = 0

Subproblem 1
Set the factor '(-6 + -1u)' equal to zero and attempt to solve:

Simplifying
-6 + -1u = 0

Solving
-6 + -1u = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1u = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1u = 0 + 6
-1u = 0 + 6

Combine like terms: 0 + 6 = 6
-1u = 6

Divide each side by '-1'.
u = -6

Simplifying
u = -6
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 = {-6, 2.666666667}