(5u+6)(2+u)=0

Solution for (5u+6)(2+u)=0 equation:

Simplifying
(5u + 6)(2 + u) = 0

Reorder the terms:
(6 + 5u)(2 + u) = 0

Multiply (6 + 5u) * (2 + u)
(6(2 + u) + 5u * (2 + u)) = 0
((2 * 6 + u * 6) + 5u * (2 + u)) = 0
((12 + 6u) + 5u * (2 + u)) = 0
(12 + 6u + (2 * 5u + u * 5u)) = 0
(12 + 6u + (10u + 5u2)) = 0

Combine like terms: 6u + 10u = 16u
(12 + 16u + 5u2) = 0

Solving
12 + 16u + 5u2 = 0

Solving for variable 'u'.

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

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

Simplifying
2 + u = 0

Solving
2 + u = 0

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

Add '-2' to each side of the equation.
2 + -2 + u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + u = 0 + -2
u = 0 + -2

Combine like terms: 0 + -2 = -2
u = -2

Simplifying
u = -2
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 = {-2, -1.2}