(2+u)(3u+8)=0

Solution for (2+u)(3u+8)=0 equation:

Simplifying
(2 + u)(3u + 8) = 0

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

Multiply (2 + u) * (8 + 3u)
(2(8 + 3u) + u(8 + 3u)) = 0
((8 * 2 + 3u * 2) + u(8 + 3u)) = 0
((16 + 6u) + u(8 + 3u)) = 0
(16 + 6u + (8 * u + 3u * u)) = 0
(16 + 6u + (8u + 3u2)) = 0

Combine like terms: 6u + 8u = 14u
(16 + 14u + 3u2) = 0

Solving
16 + 14u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(8 + 3u)(2 + u) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(2 + u)' equal to zero and attempt to solve:

Simplifying
2 + u = 0

Solving
2 + u = 0

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

Add '-2' to each side of the equation.
2 + -2 + u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + u = 0 + -2
u = 0 + -2

Combine like terms: 0 + -2 = -2
u = -2

Simplifying
u = -2
Solution
u = {-2.666666667, -2}