q^2-19q+18=0

Solution for q^2-19q+18=0 equation:

Simplifying
q2 + -19q + 18 = 0

Reorder the terms:
18 + -19q + q2 = 0

Solving
18 + -19q + q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(1 + -1q)(18 + -1q) = 0

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

Simplifying
1 + -1q = 0

Solving
1 + -1q = 0

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

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

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

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

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

Simplifying
q = 1
Subproblem 2
Set the factor '(18 + -1q)' equal to zero and attempt to solve:

Simplifying
18 + -1q = 0

Solving
18 + -1q = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1q = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1q = 0 + -18
-1q = 0 + -18

Combine like terms: 0 + -18 = -18
-1q = -18

Divide each side by '-1'.
q = 18

Simplifying
q = 18
Solution
q = {1, 18}