3v^2+4=-7v

Solution for 3v^2+4=-7v equation:

Simplifying
3v2 + 4 = -7v

Reorder the terms:
4 + 3v2 = -7v

Solving
4 + 3v2 = -7v

Solving for variable 'v'.

Reorder the terms:
4 + 7v + 3v2 = -7v + 7v

Combine like terms: -7v + 7v = 0
4 + 7v + 3v2 = 0

Factor a trinomial.
(4 + 3v)(1 + v) = 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 + 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 = {-1.333333333, -1}