(2u-9)(6+u)=0

Solution for (2u-9)(6+u)=0 equation:

Simplifying
(2u + -9)(6 + u) = 0

Reorder the terms:
(-9 + 2u)(6 + u) = 0

Multiply (-9 + 2u) * (6 + u)
(-9(6 + u) + 2u * (6 + u)) = 0
((6 * -9 + u * -9) + 2u * (6 + u)) = 0
((-54 + -9u) + 2u * (6 + u)) = 0
(-54 + -9u + (6 * 2u + u * 2u)) = 0
(-54 + -9u + (12u + 2u2)) = 0

Combine like terms: -9u + 12u = 3u
(-54 + 3u + 2u2) = 0

Solving
-54 + 3u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + -1u)(9 + -2u) = 0

Subproblem 1
Set the factor '(-6 + -1u)' equal to zero and attempt to solve:

Simplifying
-6 + -1u = 0

Solving
-6 + -1u = 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 + -1u = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1u = 0 + 6
-1u = 0 + 6

Combine like terms: 0 + 6 = 6
-1u = 6

Divide each side by '-1'.
u = -6

Simplifying
u = -6
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 = {-6, 4.5}