0=x^2-17x+72

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

Simplifying
0 = x2 + -17x + 72

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

Solving
0 = 72 + -17x + x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
-9 + x = 0

Solving
-9 + x = 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 + x = 0 + 9

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

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

Simplifying
x = 9
Subproblem 2
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
Solution
x = {9, 8}