v^2=20v-19

Solution for v^2=20v-19 equation:

Simplifying
v2 = 20v + -19

Reorder the terms:
v2 = -19 + 20v

Solving
v2 = -19 + 20v

Solving for variable 'v'.

Reorder the terms:
19 + -20v + v2 = -19 + 20v + 19 + -20v

Reorder the terms:
19 + -20v + v2 = -19 + 19 + 20v + -20v

Combine like terms: -19 + 19 = 0
19 + -20v + v2 = 0 + 20v + -20v
19 + -20v + v2 = 20v + -20v

Combine like terms: 20v + -20v = 0
19 + -20v + v2 = 0

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

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}