(3u+81)(5-u)=0

Solution for (3u+81)(5-u)=0 equation:

Simplifying
(3u + 81)(5 + -1u) = 0

Reorder the terms:
(81 + 3u)(5 + -1u) = 0

Multiply (81 + 3u) * (5 + -1u)
(81(5 + -1u) + 3u * (5 + -1u)) = 0
((5 * 81 + -1u * 81) + 3u * (5 + -1u)) = 0
((405 + -81u) + 3u * (5 + -1u)) = 0
(405 + -81u + (5 * 3u + -1u * 3u)) = 0
(405 + -81u + (15u + -3u2)) = 0

Combine like terms: -81u + 15u = -66u
(405 + -66u + -3u2) = 0

Solving
405 + -66u + -3u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3'.
3(135 + -22u + -1u2) = 0

Factor a trinomial.
3((5 + -1u)(27 + u)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + -1u)' equal to zero and attempt to solve:

Simplifying
5 + -1u = 0

Solving
5 + -1u = 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 + -1u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1u = 0 + -5
-1u = 0 + -5

Combine like terms: 0 + -5 = -5
-1u = -5

Divide each side by '-1'.
u = 5

Simplifying
u = 5
Subproblem 2
Set the factor '(27 + u)' equal to zero and attempt to solve:

Simplifying
27 + u = 0

Solving
27 + u = 0

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

Add '-27' to each side of the equation.
27 + -27 + u = 0 + -27

Combine like terms: 27 + -27 = 0
0 + u = 0 + -27
u = 0 + -27

Combine like terms: 0 + -27 = -27
u = -27

Simplifying
u = -27
Solution
u = {5, -27}