3v^2-1v=10

Solution for 3v^2-1v=10 equation:

Simplifying
3v2 + -1v = 10

Reorder the terms:
-1v + 3v2 = 10

Solving
-1v + 3v2 = 10

Solving for variable 'v'.

Reorder the terms:
-10 + -1v + 3v2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -1v + 3v2 = 0

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

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

Simplifying
-5 + -3v = 0

Solving
-5 + -3v = 0

Move all terms containing v to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -3v = 0 + 5

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

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

Divide each side by '-3'.
v = -1.666666667

Simplifying
v = -1.666666667
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 = {-1.666666667, 2}