0=-x^2+17x-72

Solution for 0=-x^2+17x-72 equation:

Simplifying
0 = -1x2 + 17x + -72

Reorder the terms:
0 = -72 + 17x + -1x2

Solving
0 = -72 + 17x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 72 = 72
72 + -17x + x2 = -72 + 17x + -1x2 + 72 + -17x + x2

Reorder the terms:
72 + -17x + x2 = -72 + 72 + 17x + -17x + -1x2 + x2

Combine like terms: -72 + 72 = 0
72 + -17x + x2 = 0 + 17x + -17x + -1x2 + x2
72 + -17x + x2 = 17x + -17x + -1x2 + x2

Combine like terms: 17x + -17x = 0
72 + -17x + x2 = 0 + -1x2 + x2
72 + -17x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
72 + -17x + x2 = 0

Factor a trinomial.
(8 + -1x)(9 + -1x) = 0

Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

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

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

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {8, 9}