(6+u)(4u+5)=0

Solution for (6+u)(4u+5)=0 equation:

Simplifying
(6 + u)(4u + 5) = 0

Reorder the terms:
(6 + u)(5 + 4u) = 0

Multiply (6 + u) * (5 + 4u)
(6(5 + 4u) + u(5 + 4u)) = 0
((5 * 6 + 4u * 6) + u(5 + 4u)) = 0
((30 + 24u) + u(5 + 4u)) = 0
(30 + 24u + (5 * u + 4u * u)) = 0
(30 + 24u + (5u + 4u2)) = 0

Combine like terms: 24u + 5u = 29u
(30 + 29u + 4u2) = 0

Solving
30 + 29u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + u)(5 + 4u) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + 4u)' equal to zero and attempt to solve:

Simplifying
5 + 4u = 0

Solving
5 + 4u = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4u = 0 + -5
4u = 0 + -5

Combine like terms: 0 + -5 = -5
4u = -5

Divide each side by '4'.
u = -1.25

Simplifying
u = -1.25
Solution
u = {-6, -1.25}