q(q+19)=-34

Solution for q(q+19)=-34 equation:

Simplifying
q(q + 19) = -34

Reorder the terms:
q(19 + q) = -34
(19 * q + q * q) = -34
(19q + q2) = -34

Solving
19q + q2 = -34

Solving for variable 'q'.

Reorder the terms:
34 + 19q + q2 = -34 + 34

Combine like terms: -34 + 34 = 0
34 + 19q + q2 = 0

Factor a trinomial.
(17 + q)(2 + q) = 0

Subproblem 1
Set the factor '(17 + q)' equal to zero and attempt to solve:

Simplifying
17 + q = 0

Solving
17 + q = 0

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

Add '-17' to each side of the equation.
17 + -17 + q = 0 + -17

Combine like terms: 17 + -17 = 0
0 + q = 0 + -17
q = 0 + -17

Combine like terms: 0 + -17 = -17
q = -17

Simplifying
q = -17
Subproblem 2
Set the factor '(2 + q)' equal to zero and attempt to solve:

Simplifying
2 + q = 0

Solving
2 + q = 0

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

Add '-2' to each side of the equation.
2 + -2 + q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + q = 0 + -2
q = 0 + -2

Combine like terms: 0 + -2 = -2
q = -2

Simplifying
q = -2
Solution
q = {-17, -2}