0=9x-20-x^2

Solution for 0=9x-20-x^2 equation:

Simplifying
0 = 9x + -20 + -1x2

Reorder the terms:
0 = -20 + 9x + -1x2

Solving
0 = -20 + 9x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 20 = 20
20 + -9x + x2 = -20 + 9x + -1x2 + 20 + -9x + x2

Reorder the terms:
20 + -9x + x2 = -20 + 20 + 9x + -9x + -1x2 + x2

Combine like terms: -20 + 20 = 0
20 + -9x + x2 = 0 + 9x + -9x + -1x2 + x2
20 + -9x + x2 = 9x + -9x + -1x2 + x2

Combine like terms: 9x + -9x = 0
20 + -9x + x2 = 0 + -1x2 + x2
20 + -9x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
20 + -9x + x2 = 0

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

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

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

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

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

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

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

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

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

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

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

Simplifying
x = 5
Solution
x = {4, 5}