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

Solution for (6+u)(4u-9)=0 equation:

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

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

Multiply (6 + u) * (-9 + 4u)
(6(-9 + 4u) + u(-9 + 4u)) = 0
((-9 * 6 + 4u * 6) + u(-9 + 4u)) = 0
((-54 + 24u) + u(-9 + 4u)) = 0
(-54 + 24u + (-9 * u + 4u * u)) = 0
(-54 + 24u + (-9u + 4u2)) = 0

Combine like terms: 24u + -9u = 15u
(-54 + 15u + 4u2) = 0

Solving
-54 + 15u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + -1u)(9 + -4u) = 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 + -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 = {-6, 2.25}