(4v+7)(6+v)=0

Solution for (4v+7)(6+v)=0 equation:

Simplifying
(4v + 7)(6 + v) = 0

Reorder the terms:
(7 + 4v)(6 + v) = 0

Multiply (7 + 4v) * (6 + v)
(7(6 + v) + 4v * (6 + v)) = 0
((6 * 7 + v * 7) + 4v * (6 + v)) = 0
((42 + 7v) + 4v * (6 + v)) = 0
(42 + 7v + (6 * 4v + v * 4v)) = 0
(42 + 7v + (24v + 4v2)) = 0

Combine like terms: 7v + 24v = 31v
(42 + 31v + 4v2) = 0

Solving
42 + 31v + 4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + v)(7 + 4v) = 0

Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 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 + v = 0 + -6

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

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

Simplifying
v = -6
Subproblem 2
Set the factor '(7 + 4v)' equal to zero and attempt to solve:

Simplifying
7 + 4v = 0

Solving
7 + 4v = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4v = 0 + -7
4v = 0 + -7

Combine like terms: 0 + -7 = -7
4v = -7

Divide each side by '4'.
v = -1.75

Simplifying
v = -1.75
Solution
v = {-6, -1.75}