3v^2+v-4=0

Solution for 3v^2+v-4=0 equation:

Simplifying
3v2 + v + -4 = 0

Reorder the terms:
-4 + v + 3v2 = 0

Solving
-4 + v + 3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-4 + -3v)(1 + -1v) = 0

Subproblem 1
Set the factor '(-4 + -3v)' equal to zero and attempt to solve:

Simplifying
-4 + -3v = 0

Solving
-4 + -3v = 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 + -3v = 0 + 4

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

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

Divide each side by '-3'.
v = -1.333333333

Simplifying
v = -1.333333333
Subproblem 2
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
Solution
v = {-1.333333333, 1}