q^2-21q=-20

Solution for q^2-21q=-20 equation:

Simplifying
q2 + -21q = -20

Reorder the terms:
-21q + q2 = -20

Solving
-21q + q2 = -20

Solving for variable 'q'.

Reorder the terms:
20 + -21q + q2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + -21q + q2 = 0

Factor a trinomial.
(1 + -1q)(20 + -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 '(20 + -1q)' equal to zero and attempt to solve:

Simplifying
20 + -1q = 0

Solving
20 + -1q = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1q = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1q = 0 + -20
-1q = 0 + -20

Combine like terms: 0 + -20 = -20
-1q = -20

Divide each side by '-1'.
q = 20

Simplifying
q = 20
Solution
q = {1, 20}