(u-11)(u+8)=-84

Solution for (u-11)(u+8)=-84 equation:

Simplifying
(u + -11)(u + 8) = -84

Reorder the terms:
(-11 + u)(u + 8) = -84

Reorder the terms:
(-11 + u)(8 + u) = -84

Multiply (-11 + u) * (8 + u)
(-11(8 + u) + u(8 + u)) = -84
((8 * -11 + u * -11) + u(8 + u)) = -84
((-88 + -11u) + u(8 + u)) = -84
(-88 + -11u + (8 * u + u * u)) = -84
(-88 + -11u + (8u + u2)) = -84

Combine like terms: -11u + 8u = -3u
(-88 + -3u + u2) = -84

Solving
-88 + -3u + u2 = -84

Solving for variable 'u'.

Reorder the terms:
-88 + 84 + -3u + u2 = -84 + 84

Combine like terms: -88 + 84 = -4
-4 + -3u + u2 = -84 + 84

Combine like terms: -84 + 84 = 0
-4 + -3u + u2 = 0

Factor a trinomial.
(-1 + -1u)(4 + -1u) = 0

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

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 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 + -1u = 0 + 1

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

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

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

Simplifying
u = -1
Subproblem 2
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
Solution
u = {-1, 4}