-x^2+22x-85=0

Solution for -x^2+22x-85=0 equation:

Simplifying
-1x2 + 22x + -85 = 0

Reorder the terms:
-85 + 22x + -1x2 = 0

Solving
-85 + 22x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-17 + x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-17 + x)' equal to zero and attempt to solve:

Simplifying
-17 + x = 0

Solving
-17 + x = 0

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

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

Combine like terms: -17 + 17 = 0
0 + x = 0 + 17
x = 0 + 17

Combine like terms: 0 + 17 = 17
x = 17

Simplifying
x = 17
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 = {17, 5}