q^2-17q=-72

Solution for q^2-17q=-72 equation:

Simplifying
q2 + -17q = -72

Reorder the terms:
-17q + q2 = -72

Solving
-17q + q2 = -72

Solving for variable 'q'.

Reorder the terms:
72 + -17q + q2 = -72 + 72

Combine like terms: -72 + 72 = 0
72 + -17q + q2 = 0

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

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

Simplifying
8 + -1q = 0

Solving
8 + -1q = 0

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

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

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

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

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

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

Simplifying
9 + -1q = 0

Solving
9 + -1q = 0

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

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

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

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

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

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