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

Solution for (3+u)(5u+6)=0 equation:

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

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

Multiply (3 + u) * (6 + 5u)
(3(6 + 5u) + u(6 + 5u)) = 0
((6 * 3 + 5u * 3) + u(6 + 5u)) = 0
((18 + 15u) + u(6 + 5u)) = 0
(18 + 15u + (6 * u + 5u * u)) = 0
(18 + 15u + (6u + 5u2)) = 0

Combine like terms: 15u + 6u = 21u
(18 + 21u + 5u2) = 0

Solving
18 + 21u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(3 + u)(6 + 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 '(6 + 5u)' equal to zero and attempt to solve:

Simplifying
6 + 5u = 0

Solving
6 + 5u = 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 + 5u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5u = 0 + -6
5u = 0 + -6

Combine like terms: 0 + -6 = -6
5u = -6

Divide each side by '5'.
u = -1.2

Simplifying
u = -1.2
Solution
u = {-3, -1.2}