(5+v)(5v+6)=0

Solution for (5+v)(5v+6)=0 equation:

Simplifying
(5 + v)(5v + 6) = 0

Reorder the terms:
(5 + v)(6 + 5v) = 0

Multiply (5 + v) * (6 + 5v)
(5(6 + 5v) + v(6 + 5v)) = 0
((6 * 5 + 5v * 5) + v(6 + 5v)) = 0
((30 + 25v) + v(6 + 5v)) = 0
(30 + 25v + (6 * v + 5v * v)) = 0
(30 + 25v + (6v + 5v2)) = 0

Combine like terms: 25v + 6v = 31v
(30 + 31v + 5v2) = 0

Solving
30 + 31v + 5v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(5 + v)(6 + 5v) = 0

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

Simplifying
5 + v = 0

Solving
5 + v = 0

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

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

Combine like terms: 5 + -5 = 0
0 + v = 0 + -5
v = 0 + -5

Combine like terms: 0 + -5 = -5
v = -5

Simplifying
v = -5
Subproblem 2
Set the factor '(6 + 5v)' equal to zero and attempt to solve:

Simplifying
6 + 5v = 0

Solving
6 + 5v = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5v = 0 + -6

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

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

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

Simplifying
v = -1.2
Solution
v = {-5, -1.2}