2v^2+11v=138

Solution for 2v^2+11v=138 equation:

Simplifying
2v2 + 11v = 138

Reorder the terms:
11v + 2v2 = 138

Solving
11v + 2v2 = 138

Solving for variable 'v'.

Reorder the terms:
-138 + 11v + 2v2 = 138 + -138

Combine like terms: 138 + -138 = 0
-138 + 11v + 2v2 = 0

Factor a trinomial.
(-23 + -2v)(6 + -1v) = 0

Subproblem 1
Set the factor '(-23 + -2v)' equal to zero and attempt to solve:

Simplifying
-23 + -2v = 0

Solving
-23 + -2v = 0

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

Add '23' to each side of the equation.
-23 + 23 + -2v = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -2v = 0 + 23
-2v = 0 + 23

Combine like terms: 0 + 23 = 23
-2v = 23

Divide each side by '-2'.
v = -11.5

Simplifying
v = -11.5
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 = {-11.5, 6}