-v^2+7v+78=0

Solution for -v^2+7v+78=0 equation:

Simplifying
-1v2 + 7v + 78 = 0

Reorder the terms:
78 + 7v + -1v2 = 0

Solving
78 + 7v + -1v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(13 + -1v)(6 + v) = 0

Subproblem 1
Set the factor '(13 + -1v)' equal to zero and attempt to solve:

Simplifying
13 + -1v = 0

Solving
13 + -1v = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1v = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1v = 0 + -13
-1v = 0 + -13

Combine like terms: 0 + -13 = -13
-1v = -13

Divide each side by '-1'.
v = 13

Simplifying
v = 13
Subproblem 2
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 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 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6
Solution
v = {13, -6}