(1[u+4]1)(1[u-7]1)=0

Solution for (1[u+4]1)(1[u-7]1)=0 equation:

Simplifying
(1[u + 4] * 1)(1[u + -7] * 1) = 0

Reorder the terms:
(1[4 + u] * 1)(1[u + -7] * 1) = 0

Reorder the terms for easier multiplication:
(1 * 1[4 + u])(1[u + -7] * 1) = 0

Multiply 1 * 1
(1[4 + u])(1[u + -7] * 1) = 0
([4 * 1 + u * 1])(1[u + -7] * 1) = 0
([4 + 1u])(1[u + -7] * 1) = 0

Reorder the terms:
(4 + 1u)(1[-7 + u] * 1) = 0

Reorder the terms for easier multiplication:
(4 + 1u)(1 * 1[-7 + u]) = 0

Multiply 1 * 1
(4 + 1u)(1[-7 + u]) = 0
(4 + 1u)([-7 * 1 + u * 1]) = 0
(4 + 1u)([-7 + 1u]) = 0

Multiply (4 + 1u) * (-7 + 1u)
(4(-7 + 1u) + 1u * (-7 + 1u)) = 0
((-7 * 4 + 1u * 4) + 1u * (-7 + 1u)) = 0
((-28 + 4u) + 1u * (-7 + 1u)) = 0
(-28 + 4u + (-7 * 1u + 1u * 1u)) = 0
(-28 + 4u + (-7u + 1u2)) = 0

Combine like terms: 4u + -7u = -3u
(-28 + -3u + 1u2) = 0

Solving
-28 + -3u + 1u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-4 + -1u)(7 + -1u) = 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 '(7 + -1u)' equal to zero and attempt to solve:

Simplifying
7 + -1u = 0

Solving
7 + -1u = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1u = 0 + -7
-1u = 0 + -7

Combine like terms: 0 + -7 = -7
-1u = -7

Divide each side by '-1'.
u = 7

Simplifying
u = 7
Solution
u = {-4, 7}