v^2-20v+45=-6

Solution for v^2-20v+45=-6 equation:

Simplifying
v2 + -20v + 45 = -6

Reorder the terms:
45 + -20v + v2 = -6

Solving
45 + -20v + v2 = -6

Solving for variable 'v'.

Reorder the terms:
45 + 6 + -20v + v2 = -6 + 6

Combine like terms: 45 + 6 = 51
51 + -20v + v2 = -6 + 6

Combine like terms: -6 + 6 = 0
51 + -20v + v2 = 0

Factor a trinomial.
(3 + -1v)(17 + -1v) = 0

Subproblem 1
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Subproblem 2
Set the factor '(17 + -1v)' equal to zero and attempt to solve:

Simplifying
17 + -1v = 0

Solving
17 + -1v = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1v = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1v = 0 + -17
-1v = 0 + -17

Combine like terms: 0 + -17 = -17
-1v = -17

Divide each side by '-1'.
v = 17

Simplifying
v = 17
Solution
v = {3, 17}