6v^2=-1-7v

Solution for 6v^2=-1-7v equation:

Simplifying
6v2 = -1 + -7v

Solving
6v2 = -1 + -7v

Solving for variable 'v'.

Reorder the terms:
1 + 7v + 6v2 = -1 + -7v + 1 + 7v

Reorder the terms:
1 + 7v + 6v2 = -1 + 1 + -7v + 7v

Combine like terms: -1 + 1 = 0
1 + 7v + 6v2 = 0 + -7v + 7v
1 + 7v + 6v2 = -7v + 7v

Combine like terms: -7v + 7v = 0
1 + 7v + 6v2 = 0

Factor a trinomial.
(1 + v)(1 + 6v) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 6v)' equal to zero and attempt to solve:

Simplifying
1 + 6v = 0

Solving
1 + 6v = 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 + 6v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6v = 0 + -1
6v = 0 + -1

Combine like terms: 0 + -1 = -1
6v = -1

Divide each side by '6'.
v = -0.1666666667

Simplifying
v = -0.1666666667
Solution
v = {-1, -0.1666666667}