5v^2+13v=6

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

Simplifying
5v2 + 13v = 6

Reorder the terms:
13v + 5v2 = 6

Solving
13v + 5v2 = 6

Solving for variable 'v'.

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

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

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

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

Simplifying
-3 + -1v = 0

Solving
-3 + -1v = 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 + -1v = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1v = 0 + 3
-1v = 0 + 3

Combine like terms: 0 + 3 = 3
-1v = 3

Divide each side by '-1'.
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}