5v^2=-6+13v

Solution for 5v^2=-6+13v equation:

Simplifying
5v2 = -6 + 13v

Solving
5v2 = -6 + 13v

Solving for variable 'v'.

Reorder the terms:
6 + -13v + 5v2 = -6 + 13v + 6 + -13v

Reorder the terms:
6 + -13v + 5v2 = -6 + 6 + 13v + -13v

Combine like terms: -6 + 6 = 0
6 + -13v + 5v2 = 0 + 13v + -13v
6 + -13v + 5v2 = 13v + -13v

Combine like terms: 13v + -13v = 0
6 + -13v + 5v2 = 0

Factor a trinomial.
(3 + -5v)(2 + -1v) = 0

Subproblem 1
Set the factor '(3 + -5v)' equal to zero and attempt to solve:

Simplifying
3 + -5v = 0

Solving
3 + -5v = 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 + -5v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5v = 0 + -3
-5v = 0 + -3

Combine like terms: 0 + -3 = -3
-5v = -3

Divide each side by '-5'.
v = 0.6

Simplifying
v = 0.6
Subproblem 2
Set the factor '(2 + -1v)' equal to zero and attempt to solve:

Simplifying
2 + -1v = 0

Solving
2 + -1v = 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 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2
Solution
v = {0.6, 2}