(4u-9)(4+u)=0

Solution for (4u-9)(4+u)=0 equation:

Simplifying
(4u + -9)(4 + u) = 0

Reorder the terms:
(-9 + 4u)(4 + u) = 0

Multiply (-9 + 4u) * (4 + u)
(-9(4 + u) + 4u * (4 + u)) = 0
((4 * -9 + u * -9) + 4u * (4 + u)) = 0
((-36 + -9u) + 4u * (4 + u)) = 0
(-36 + -9u + (4 * 4u + u * 4u)) = 0
(-36 + -9u + (16u + 4u2)) = 0

Combine like terms: -9u + 16u = 7u
(-36 + 7u + 4u2) = 0

Solving
-36 + 7u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-4 + -1u)(9 + -4u) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -4u)' equal to zero and attempt to solve:

Simplifying
9 + -4u = 0

Solving
9 + -4u = 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 + -4u = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4u = 0 + -9
-4u = 0 + -9

Combine like terms: 0 + -9 = -9
-4u = -9

Divide each side by '-4'.
u = 2.25

Simplifying
u = 2.25
Solution
u = {-4, 2.25}