1q^2+19=-20q

Solution for 1q^2+19=-20q equation:

Simplifying
1q2 + 19 = -20q

Reorder the terms:
19 + 1q2 = -20q

Solving
19 + 1q2 = -20q

Solving for variable 'q'.

Reorder the terms:
19 + 20q + 1q2 = -20q + 20q

Combine like terms: -20q + 20q = 0
19 + 20q + 1q2 = 0

Factor a trinomial.
(19 + q)(1 + q) = 0

Subproblem 1
Set the factor '(19 + q)' equal to zero and attempt to solve:

Simplifying
19 + q = 0

Solving
19 + q = 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 + q = 0 + -19

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

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

Simplifying
q = -19
Subproblem 2
Set the factor '(1 + q)' equal to zero and attempt to solve:

Simplifying
1 + q = 0

Solving
1 + q = 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 + q = 0 + -1

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

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

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