3v^2=-7v-2

Solution for 3v^2=-7v-2 equation:

Simplifying
3v2 = -7v + -2

Reorder the terms:
3v2 = -2 + -7v

Solving
3v2 = -2 + -7v

Solving for variable 'v'.

Reorder the terms:
2 + 7v + 3v2 = -2 + -7v + 2 + 7v

Reorder the terms:
2 + 7v + 3v2 = -2 + 2 + -7v + 7v

Combine like terms: -2 + 2 = 0
2 + 7v + 3v2 = 0 + -7v + 7v
2 + 7v + 3v2 = -7v + 7v

Combine like terms: -7v + 7v = 0
2 + 7v + 3v2 = 0

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

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

Simplifying
2 + v = 0

Solving
2 + v = 0

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

Add '-2' to each side of the equation.
2 + -2 + v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + v = 0 + -2
v = 0 + -2

Combine like terms: 0 + -2 = -2
v = -2

Simplifying
v = -2
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 = {-2, -0.3333333333}