3v(v-2)=11v+6

Solution for 3v(v-2)=11v+6 equation:

Simplifying
3v(v + -2) = 11v + 6

Reorder the terms:
3v(-2 + v) = 11v + 6
(-2 * 3v + v * 3v) = 11v + 6
(-6v + 3v2) = 11v + 6

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

Solving
-6v + 3v2 = 6 + 11v

Solving for variable 'v'.

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

Combine like terms: -6v + -11v = -17v
-6 + -17v + 3v2 = 6 + 11v + -6 + -11v

Reorder the terms:
-6 + -17v + 3v2 = 6 + -6 + 11v + -11v

Combine like terms: 6 + -6 = 0
-6 + -17v + 3v2 = 0 + 11v + -11v
-6 + -17v + 3v2 = 11v + -11v

Combine like terms: 11v + -11v = 0
-6 + -17v + 3v2 = 0

Factor a trinomial.
(-1 + -3v)(6 + -1v) = 0

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

Simplifying
-1 + -3v = 0

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

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

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

Divide each side by '-3'.
v = -0.3333333333

Simplifying
v = -0.3333333333
Subproblem 2
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v = 0 + -6
-1v = 0 + -6

Combine like terms: 0 + -6 = -6
-1v = -6

Divide each side by '-1'.
v = 6

Simplifying
v = 6
Solution
v = {-0.3333333333, 6}