10v^2=13v+3

Solution for 10v^2=13v+3 equation:

Simplifying
10v2 = 13v + 3

Reorder the terms:
10v2 = 3 + 13v

Solving
10v2 = 3 + 13v

Solving for variable 'v'.

Reorder the terms:
-3 + -13v + 10v2 = 3 + 13v + -3 + -13v

Reorder the terms:
-3 + -13v + 10v2 = 3 + -3 + 13v + -13v

Combine like terms: 3 + -3 = 0
-3 + -13v + 10v2 = 0 + 13v + -13v
-3 + -13v + 10v2 = 13v + -13v

Combine like terms: 13v + -13v = 0
-3 + -13v + 10v2 = 0

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

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

Simplifying
-1 + -5v = 0

Solving
-1 + -5v = 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 + -5v = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5v = 0 + 1
-5v = 0 + 1

Combine like terms: 0 + 1 = 1
-5v = 1

Divide each side by '-5'.
v = -0.2

Simplifying
v = -0.2
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 = {-0.2, 1.5}