2v^2+6=-7v

Solution for 2v^2+6=-7v equation:

Simplifying
2v2 + 6 = -7v

Reorder the terms:
6 + 2v2 = -7v

Solving
6 + 2v2 = -7v

Solving for variable 'v'.

Reorder the terms:
6 + 7v + 2v2 = -7v + 7v

Combine like terms: -7v + 7v = 0
6 + 7v + 2v2 = 0

Factor a trinomial.
(2 + v)(3 + 2v) = 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 '(3 + 2v)' equal to zero and attempt to solve:

Simplifying
3 + 2v = 0

Solving
3 + 2v = 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 + 2v = 0 + -3

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

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

Divide each side by '2'.
v = -1.5

Simplifying
v = -1.5
Solution
v = {-2, -1.5}