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

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

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

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

Multiply (4 + v) * (6 + 4v)
(4(6 + 4v) + v(6 + 4v)) = 0
((6 * 4 + 4v * 4) + v(6 + 4v)) = 0
((24 + 16v) + v(6 + 4v)) = 0
(24 + 16v + (6 * v + 4v * v)) = 0
(24 + 16v + (6v + 4v2)) = 0

Combine like terms: 16v + 6v = 22v
(24 + 22v + 4v2) = 0

Solving
24 + 22v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 11v + 2v2) = 0

Factor a trinomial.
2((4 + v)(3 + 2v)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + v)' equal to zero and attempt to solve:

Simplifying
4 + v = 0

Solving
4 + v = 0

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

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

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

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

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

Simplifying
3 + 2v = 0

Solving
3 + 2v = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2v = 0 + -3
2v = 0 + -3

Combine like terms: 0 + -3 = -3
2v = -3

Divide each side by '2'.
v = -1.5

Simplifying
v = -1.5
Solution
v = {-4, -1.5}