7v^2+24v+9=0

Solution for 7v^2+24v+9=0 equation:

Simplifying
7v2 + 24v + 9 = 0

Reorder the terms:
9 + 24v + 7v2 = 0

Solving
9 + 24v + 7v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(3 + v)(3 + 7v) = 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 '(3 + 7v)' equal to zero and attempt to solve:

Simplifying
3 + 7v = 0

Solving
3 + 7v = 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 + 7v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7v = 0 + -3
7v = 0 + -3

Combine like terms: 0 + -3 = -3
7v = -3

Divide each side by '7'.
v = -0.4285714286

Simplifying
v = -0.4285714286
Solution
v = {-3, -0.4285714286}