3v^2-11v=14

Solution for 3v^2-11v=14 equation:

Simplifying
3v2 + -11v = 14

Reorder the terms:
-11v + 3v2 = 14

Solving
-11v + 3v2 = 14

Solving for variable 'v'.

Reorder the terms:
-14 + -11v + 3v2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -11v + 3v2 = 0

Factor a trinomial.
(-1 + -1v)(14 + -3v) = 0

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

Simplifying
-1 + -1v = 0

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

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

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

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

Simplifying
v = -1
Subproblem 2
Set the factor '(14 + -3v)' equal to zero and attempt to solve:

Simplifying
14 + -3v = 0

Solving
14 + -3v = 0

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

Add '-14' to each side of the equation.
14 + -14 + -3v = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -3v = 0 + -14
-3v = 0 + -14

Combine like terms: 0 + -14 = -14
-3v = -14

Divide each side by '-3'.
v = 4.666666667

Simplifying
v = 4.666666667
Solution
v = {-1, 4.666666667}