4v^2+49v+111=0

Solution for 4v^2+49v+111=0 equation:

Simplifying
4v2 + 49v + 111 = 0

Reorder the terms:
111 + 49v + 4v2 = 0

Solving
111 + 49v + 4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(37 + 4v)(3 + v) = 0

Subproblem 1
Set the factor '(37 + 4v)' equal to zero and attempt to solve:

Simplifying
37 + 4v = 0

Solving
37 + 4v = 0

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

Add '-37' to each side of the equation.
37 + -37 + 4v = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 4v = 0 + -37
4v = 0 + -37

Combine like terms: 0 + -37 = -37
4v = -37

Divide each side by '4'.
v = -9.25

Simplifying
v = -9.25
Subproblem 2
Set the factor '(3 + v)' equal to zero and attempt to solve:

Simplifying
3 + v = 0

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

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

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

Simplifying
v = -3
Solution
v = {-9.25, -3}