(3-u)(u+6)=0

Solution for (3-u)(u+6)=0 equation:

Simplifying
(3 + -1u)(u + 6) = 0

Reorder the terms:
(3 + -1u)(6 + u) = 0

Multiply (3 + -1u) * (6 + u)
(3(6 + u) + -1u * (6 + u)) = 0
((6 * 3 + u * 3) + -1u * (6 + u)) = 0
((18 + 3u) + -1u * (6 + u)) = 0
(18 + 3u + (6 * -1u + u * -1u)) = 0
(18 + 3u + (-6u + -1u2)) = 0

Combine like terms: 3u + -6u = -3u
(18 + -3u + -1u2) = 0

Solving
18 + -3u + -1u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(3 + -1u)(6 + u) = 0

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

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Subproblem 2
Set the factor '(6 + u)' equal to zero and attempt to solve:

Simplifying
6 + u = 0

Solving
6 + u = 0

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

Add '-6' to each side of the equation.
6 + -6 + u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + u = 0 + -6
u = 0 + -6

Combine like terms: 0 + -6 = -6
u = -6

Simplifying
u = -6
Solution
u = {3, -6}