v^2-18v+77=5

Solution for v^2-18v+77=5 equation:

Simplifying
v2 + -18v + 77 = 5

Reorder the terms:
77 + -18v + v2 = 5

Solving
77 + -18v + v2 = 5

Solving for variable 'v'.

Reorder the terms:
77 + -5 + -18v + v2 = 5 + -5

Combine like terms: 77 + -5 = 72
72 + -18v + v2 = 5 + -5

Combine like terms: 5 + -5 = 0
72 + -18v + v2 = 0

Factor a trinomial.
(6 + -1v)(12 + -1v) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(12 + -1v)' equal to zero and attempt to solve:

Simplifying
12 + -1v = 0

Solving
12 + -1v = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1v = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1v = 0 + -12
-1v = 0 + -12

Combine like terms: 0 + -12 = -12
-1v = -12

Divide each side by '-1'.
v = 12

Simplifying
v = 12
Solution
v = {6, 12}