4v^2-72v-76=0

Solution for 4v^2-72v-76=0 equation:

Simplifying
4v2 + -72v + -76 = 0

Reorder the terms:
-76 + -72v + 4v2 = 0

Solving
-76 + -72v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-19 + -18v + v2) = 0

Factor a trinomial.
4((-1 + -1v)(19 + -1v)) = 0

Ignore the factor 4.
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 '(19 + -1v)' equal to zero and attempt to solve:

Simplifying
19 + -1v = 0

Solving
19 + -1v = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1v = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1v = 0 + -19
-1v = 0 + -19

Combine like terms: 0 + -19 = -19
-1v = -19

Divide each side by '-1'.
v = 19

Simplifying
v = 19
Solution
v = {-1, 19}