3v^2=-13v-4

Solution for 3v^2=-13v-4 equation:

Simplifying
3v2 = -13v + -4

Reorder the terms:
3v2 = -4 + -13v

Solving
3v2 = -4 + -13v

Solving for variable 'v'.

Reorder the terms:
4 + 13v + 3v2 = -4 + -13v + 4 + 13v

Reorder the terms:
4 + 13v + 3v2 = -4 + 4 + -13v + 13v

Combine like terms: -4 + 4 = 0
4 + 13v + 3v2 = 0 + -13v + 13v
4 + 13v + 3v2 = -13v + 13v

Combine like terms: -13v + 13v = 0
4 + 13v + 3v2 = 0

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

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

Simplifying
4 + v = 0

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

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

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

Simplifying
v = -4
Subproblem 2
Set the factor '(1 + 3v)' equal to zero and attempt to solve:

Simplifying
1 + 3v = 0

Solving
1 + 3v = 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 + 3v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3v = 0 + -1
3v = 0 + -1

Combine like terms: 0 + -1 = -1
3v = -1

Divide each side by '3'.
v = -0.3333333333

Simplifying
v = -0.3333333333
Solution
v = {-4, -0.3333333333}