v^2=-v+20

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

Simplifying
v2 = -1v + 20

Reorder the terms:
v2 = 20 + -1v

Solving
v2 = 20 + -1v

Solving for variable 'v'.

Reorder the terms:
-20 + v + v2 = 20 + -1v + -20 + v

Reorder the terms:
-20 + v + v2 = 20 + -20 + -1v + v

Combine like terms: 20 + -20 = 0
-20 + v + v2 = 0 + -1v + v
-20 + v + v2 = -1v + v

Combine like terms: -1v + v = 0
-20 + v + v2 = 0

Factor a trinomial.
(-5 + -1v)(4 + -1v) = 0

Subproblem 1
Set the factor '(-5 + -1v)' equal to zero and attempt to solve:

Simplifying
-5 + -1v = 0

Solving
-5 + -1v = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1v = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1v = 0 + 5
-1v = 0 + 5

Combine like terms: 0 + 5 = 5
-1v = 5

Divide each side by '-1'.
v = -5

Simplifying
v = -5
Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {-5, 4}