q^2-18q+45=0

Solution for q^2-18q+45=0 equation:

Simplifying
q2 + -18q + 45 = 0

Reorder the terms:
45 + -18q + q2 = 0

Solving
45 + -18q + q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(3 + -1q)(15 + -1q) = 0

Subproblem 1
Set the factor '(3 + -1q)' equal to zero and attempt to solve:

Simplifying
3 + -1q = 0

Solving
3 + -1q = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1q = 0 + -3
-1q = 0 + -3

Combine like terms: 0 + -3 = -3
-1q = -3

Divide each side by '-1'.
q = 3

Simplifying
q = 3
Subproblem 2
Set the factor '(15 + -1q)' equal to zero and attempt to solve:

Simplifying
15 + -1q = 0

Solving
15 + -1q = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1q = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1q = 0 + -15
-1q = 0 + -15

Combine like terms: 0 + -15 = -15
-1q = -15

Divide each side by '-1'.
q = 15

Simplifying
q = 15
Solution
q = {3, 15}