3v^2=11v+4

Solution for 3v^2=11v+4 equation:

Simplifying
3v2 = 11v + 4

Reorder the terms:
3v2 = 4 + 11v

Solving
3v2 = 4 + 11v

Solving for variable 'v'.

Reorder the terms:
-4 + -11v + 3v2 = 4 + 11v + -4 + -11v

Reorder the terms:
-4 + -11v + 3v2 = 4 + -4 + 11v + -11v

Combine like terms: 4 + -4 = 0
-4 + -11v + 3v2 = 0 + 11v + -11v
-4 + -11v + 3v2 = 11v + -11v

Combine like terms: 11v + -11v = 0
-4 + -11v + 3v2 = 0

Factor a trinomial.
(-1 + -3v)(4 + -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 '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {-0.3333333333, 4}