3v^2=11v-6

Solution for 3v^2=11v-6 equation:

Simplifying
3v2 = 11v + -6

Reorder the terms:
3v2 = -6 + 11v

Solving
3v2 = -6 + 11v

Solving for variable 'v'.

Reorder the terms:
6 + -11v + 3v2 = -6 + 11v + 6 + -11v

Reorder the terms:
6 + -11v + 3v2 = -6 + 6 + 11v + -11v

Combine like terms: -6 + 6 = 0
6 + -11v + 3v2 = 0 + 11v + -11v
6 + -11v + 3v2 = 11v + -11v

Combine like terms: 11v + -11v = 0
6 + -11v + 3v2 = 0

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

Subproblem 1
Set the factor '(2 + -3v)' equal to zero and attempt to solve:

Simplifying
2 + -3v = 0

Solving
2 + -3v = 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 + -3v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3v = 0 + -2
-3v = 0 + -2

Combine like terms: 0 + -2 = -2
-3v = -2

Divide each side by '-3'.
v = 0.6666666667

Simplifying
v = 0.6666666667
Subproblem 2
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
Solution
v = {0.6666666667, 3}