4v^2-19v=5

Solution for 4v^2-19v=5 equation:

Simplifying
4v2 + -19v = 5

Reorder the terms:
-19v + 4v2 = 5

Solving
-19v + 4v2 = 5

Solving for variable 'v'.

Reorder the terms:
-5 + -19v + 4v2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -19v + 4v2 = 0

Factor a trinomial.
(-1 + -4v)(5 + -1v) = 0

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

Simplifying
-1 + -4v = 0

Solving
-1 + -4v = 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 + -4v = 0 + 1

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

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

Divide each side by '-4'.
v = -0.25

Simplifying
v = -0.25
Subproblem 2
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Solution
v = {-0.25, 5}