(1[8+u]1)(1[2u+1]1)=0

Solution for (1[8+u]1)(1[2u+1]1)=0 equation:

Simplifying
(1[8 + u] * 1)(1[2u + 1] * 1) = 0

Reorder the terms for easier multiplication:
(1 * 1[8 + u])(1[2u + 1] * 1) = 0

Multiply 1 * 1
(1[8 + u])(1[2u + 1] * 1) = 0
([8 * 1 + u * 1])(1[2u + 1] * 1) = 0
([8 + 1u])(1[2u + 1] * 1) = 0

Reorder the terms:
(8 + 1u)(1[1 + 2u] * 1) = 0

Reorder the terms for easier multiplication:
(8 + 1u)(1 * 1[1 + 2u]) = 0

Multiply 1 * 1
(8 + 1u)(1[1 + 2u]) = 0
(8 + 1u)([1 * 1 + 2u * 1]) = 0
(8 + 1u)([1 + 2u]) = 0

Multiply (8 + 1u) * (1 + 2u)
(8(1 + 2u) + 1u * (1 + 2u)) = 0
((1 * 8 + 2u * 8) + 1u * (1 + 2u)) = 0
((8 + 16u) + 1u * (1 + 2u)) = 0
(8 + 16u + (1 * 1u + 2u * 1u)) = 0
(8 + 16u + (1u + 2u2)) = 0

Combine like terms: 16u + 1u = 17u
(8 + 17u + 2u2) = 0

Solving
8 + 17u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(8 + u)(1 + 2u) = 0

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

Simplifying
8 + u = 0

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

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

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

Simplifying
u = -8
Subproblem 2
Set the factor '(1 + 2u)' equal to zero and attempt to solve:

Simplifying
1 + 2u = 0

Solving
1 + 2u = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2u = 0 + -1
2u = 0 + -1

Combine like terms: 0 + -1 = -1
2u = -1

Divide each side by '2'.
u = -0.5

Simplifying
u = -0.5
Solution
u = {-8, -0.5}