4v^2+11v+6=0

Solution for 4v^2+11v+6=0 equation:

Simplifying
4v2 + 11v + 6 = 0

Reorder the terms:
6 + 11v + 4v2 = 0

Solving
6 + 11v + 4v2 = 0

Solving for variable 'v'.

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

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

Simplifying
2 + v = 0

Solving
2 + v = 0

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

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

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

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

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

Simplifying
3 + 4v = 0

Solving
3 + 4v = 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 + 4v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4v = 0 + -3
4v = 0 + -3

Combine like terms: 0 + -3 = -3
4v = -3

Divide each side by '4'.
v = -0.75

Simplifying
v = -0.75
Solution
v = {-2, -0.75}