21v^2+31v+4=0

Solution for 21v^2+31v+4=0 equation:

Simplifying
21v2 + 31v + 4 = 0

Reorder the terms:
4 + 31v + 21v2 = 0

Solving
4 + 31v + 21v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(4 + 3v)(1 + 7v) = 0

Subproblem 1
Set the factor '(4 + 3v)' equal to zero and attempt to solve:

Simplifying
4 + 3v = 0

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

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

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

Divide each side by '3'.
v = -1.333333333

Simplifying
v = -1.333333333
Subproblem 2
Set the factor '(1 + 7v)' equal to zero and attempt to solve:

Simplifying
1 + 7v = 0

Solving
1 + 7v = 0

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

Add '-1' to each side of the equation.
1 + -1 + 7v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7v = 0 + -1
7v = 0 + -1

Combine like terms: 0 + -1 = -1
7v = -1

Divide each side by '7'.
v = -0.1428571429

Simplifying
v = -0.1428571429
Solution
v = {-1.333333333, -0.1428571429}