4v^2+25v+21=0

Solution for 4v^2+25v+21=0 equation:

Simplifying
4v2 + 25v + 21 = 0

Reorder the terms:
21 + 25v + 4v2 = 0

Solving
21 + 25v + 4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(21 + 4v)(1 + v) = 0

Subproblem 1
Set the factor '(21 + 4v)' equal to zero and attempt to solve:

Simplifying
21 + 4v = 0

Solving
21 + 4v = 0

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

Add '-21' to each side of the equation.
21 + -21 + 4v = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 4v = 0 + -21
4v = 0 + -21

Combine like terms: 0 + -21 = -21
4v = -21

Divide each side by '4'.
v = -5.25

Simplifying
v = -5.25
Subproblem 2
Set the factor '(1 + v)' equal to zero and attempt to solve:

Simplifying
1 + v = 0

Solving
1 + v = 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 + v = 0 + -1

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

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

Simplifying
v = -1
Solution
v = {-5.25, -1}