4v^2+19v+21=0

Solution for 4v^2+19v+21=0 equation:

Simplifying
4v2 + 19v + 21 = 0

Reorder the terms:
21 + 19v + 4v2 = 0

Solving
21 + 19v + 4v2 = 0

Solving for variable 'v'.

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

Subproblem 1
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
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 = {-3, -1.75}