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

Solution for (3+u)(5u+4)=0 equation:

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

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

Multiply (3 + u) * (4 + 5u)
(3(4 + 5u) + u(4 + 5u)) = 0
((4 * 3 + 5u * 3) + u(4 + 5u)) = 0
((12 + 15u) + u(4 + 5u)) = 0
(12 + 15u + (4 * u + 5u * u)) = 0
(12 + 15u + (4u + 5u2)) = 0

Combine like terms: 15u + 4u = 19u
(12 + 19u + 5u2) = 0

Solving
12 + 19u + 5u2 = 0

Solving for variable 'u'.

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

Subproblem 1
Set the factor '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 0

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

Add '-3' to each side of the equation.
3 + -3 + u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + u = 0 + -3
u = 0 + -3

Combine like terms: 0 + -3 = -3
u = -3

Simplifying
u = -3
Subproblem 2
Set the factor '(4 + 5u)' equal to zero and attempt to solve:

Simplifying
4 + 5u = 0

Solving
4 + 5u = 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 + 5u = 0 + -4

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

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

Divide each side by '5'.
u = -0.8

Simplifying
u = -0.8
Solution
u = {-3, -0.8}