6v^2+6=v^2-17v

Solution for 6v^2+6=v^2-17v equation:

Simplifying
6v2 + 6 = v2 + -17v

Reorder the terms:
6 + 6v2 = v2 + -17v

Reorder the terms:
6 + 6v2 = -17v + v2

Solving
6 + 6v2 = -17v + v2

Solving for variable 'v'.

Reorder the terms:
6 + 17v + 6v2 + -1v2 = -17v + v2 + 17v + -1v2

Combine like terms: 6v2 + -1v2 = 5v2
6 + 17v + 5v2 = -17v + v2 + 17v + -1v2

Reorder the terms:
6 + 17v + 5v2 = -17v + 17v + v2 + -1v2

Combine like terms: -17v + 17v = 0
6 + 17v + 5v2 = 0 + v2 + -1v2
6 + 17v + 5v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
6 + 17v + 5v2 = 0

Factor a trinomial.
(3 + v)(2 + 5v) = 0

Subproblem 1
Set the factor '(3 + v)' equal to zero and attempt to solve:

Simplifying
3 + v = 0

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

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

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

Simplifying
v = -3
Subproblem 2
Set the factor '(2 + 5v)' equal to zero and attempt to solve:

Simplifying
2 + 5v = 0

Solving
2 + 5v = 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 + 5v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5v = 0 + -2
5v = 0 + -2

Combine like terms: 0 + -2 = -2
5v = -2

Divide each side by '5'.
v = -0.4

Simplifying
v = -0.4
Solution
v = {-3, -0.4}