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

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

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

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

Multiply (2 + u) * (-9 + 2u)
(2(-9 + 2u) + u(-9 + 2u)) = 0
((-9 * 2 + 2u * 2) + u(-9 + 2u)) = 0
((-18 + 4u) + u(-9 + 2u)) = 0
(-18 + 4u + (-9 * u + 2u * u)) = 0
(-18 + 4u + (-9u + 2u2)) = 0

Combine like terms: 4u + -9u = -5u
(-18 + -5u + 2u2) = 0

Solving
-18 + -5u + 2u2 = 0

Solving for variable 'u'.

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

Subproblem 1
Set the factor '(-2 + -1u)' equal to zero and attempt to solve:

Simplifying
-2 + -1u = 0

Solving
-2 + -1u = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1u = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1u = 0 + 2
-1u = 0 + 2

Combine like terms: 0 + 2 = 2
-1u = 2

Divide each side by '-1'.
u = -2

Simplifying
u = -2
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 = {-2, 4.5}