4v^2-38v+84=0

Solution for 4v^2-38v+84=0 equation:

Simplifying
4v2 + -38v + 84 = 0

Reorder the terms:
84 + -38v + 4v2 = 0

Solving
84 + -38v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(42 + -19v + 2v2) = 0

Factor a trinomial.
2((7 + -2v)(6 + -1v)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -2v)' equal to zero and attempt to solve:

Simplifying
7 + -2v = 0

Solving
7 + -2v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2v = 0 + -7
-2v = 0 + -7

Combine like terms: 0 + -7 = -7
-2v = -7

Divide each side by '-2'.
v = 3.5

Simplifying
v = 3.5
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 = {3.5, 6}