q^2-14q+45=0

Solution for q^2-14q+45=0 equation:

Simplifying
q2 + -14q + 45 = 0

Reorder the terms:
45 + -14q + q2 = 0

Solving
45 + -14q + q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(5 + -1q)(9 + -1q) = 0

Subproblem 1
Set the factor '(5 + -1q)' equal to zero and attempt to solve:

Simplifying
5 + -1q = 0

Solving
5 + -1q = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1q = 0 + -5
-1q = 0 + -5

Combine like terms: 0 + -5 = -5
-1q = -5

Divide each side by '-1'.
q = 5

Simplifying
q = 5
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 = {5, 9}