(1[5+u]1)(1[2u+9]1)=0

Solution for (1[5+u]1)(1[2u+9]1)=0 equation:

Simplifying
(1[5 + u] * 1)(1[2u + 9] * 1) = 0

Reorder the terms for easier multiplication:
(1 * 1[5 + u])(1[2u + 9] * 1) = 0

Multiply 1 * 1
(1[5 + u])(1[2u + 9] * 1) = 0
([5 * 1 + u * 1])(1[2u + 9] * 1) = 0
([5 + 1u])(1[2u + 9] * 1) = 0

Reorder the terms:
(5 + 1u)(1[9 + 2u] * 1) = 0

Reorder the terms for easier multiplication:
(5 + 1u)(1 * 1[9 + 2u]) = 0

Multiply 1 * 1
(5 + 1u)(1[9 + 2u]) = 0
(5 + 1u)([9 * 1 + 2u * 1]) = 0
(5 + 1u)([9 + 2u]) = 0

Multiply (5 + 1u) * (9 + 2u)
(5(9 + 2u) + 1u * (9 + 2u)) = 0
((9 * 5 + 2u * 5) + 1u * (9 + 2u)) = 0
((45 + 10u) + 1u * (9 + 2u)) = 0
(45 + 10u + (9 * 1u + 2u * 1u)) = 0
(45 + 10u + (9u + 2u2)) = 0

Combine like terms: 10u + 9u = 19u
(45 + 19u + 2u2) = 0

Solving
45 + 19u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(5 + u)(9 + 2u) = 0

Subproblem 1
Set the factor '(5 + u)' equal to zero and attempt to solve:

Simplifying
5 + u = 0

Solving
5 + u = 0

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

Add '-5' to each side of the equation.
5 + -5 + u = 0 + -5

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

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

Simplifying
u = -5
Subproblem 2
Set the factor '(9 + 2u)' equal to zero and attempt to solve:

Simplifying
9 + 2u = 0

Solving
9 + 2u = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2u = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2u = 0 + -9
2u = 0 + -9

Combine like terms: 0 + -9 = -9
2u = -9

Divide each side by '2'.
u = -4.5

Simplifying
u = -4.5
Solution
u = {-5, -4.5}