q^2+19=20q

Solution for q^2+19=20q equation:

Simplifying
q2 + 19 = 20q

Reorder the terms:
19 + q2 = 20q

Solving
19 + q2 = 20q

Solving for variable 'q'.

Reorder the terms:
19 + -20q + q2 = 20q + -20q

Combine like terms: 20q + -20q = 0
19 + -20q + q2 = 0

Factor a trinomial.
(1 + -1q)(19 + -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 '(19 + -1q)' equal to zero and attempt to solve:

Simplifying
19 + -1q = 0

Solving
19 + -1q = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1q = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1q = 0 + -19
-1q = 0 + -19

Combine like terms: 0 + -19 = -19
-1q = -19

Divide each side by '-1'.
q = 19

Simplifying
q = 19
Solution
q = {1, 19}