(q+4)(q+5)=0

Solution for (q+4)(q+5)=0 equation:

Simplifying
(q + 4)(q + 5) = 0

Reorder the terms:
(4 + q)(q + 5) = 0

Reorder the terms:
(4 + q)(5 + q) = 0

Multiply (4 + q) * (5 + q)
(4(5 + q) + q(5 + q)) = 0
((5 * 4 + q * 4) + q(5 + q)) = 0
((20 + 4q) + q(5 + q)) = 0
(20 + 4q + (5 * q + q * q)) = 0
(20 + 4q + (5q + q2)) = 0

Combine like terms: 4q + 5q = 9q
(20 + 9q + q2) = 0

Solving
20 + 9q + q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(5 + q)(4 + q) = 0

Subproblem 1
Set the factor '(5 + q)' equal to zero and attempt to solve:

Simplifying
5 + q = 0

Solving
5 + q = 0

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

Add '-5' to each side of the equation.
5 + -5 + q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + q = 0 + -5
q = 0 + -5

Combine like terms: 0 + -5 = -5
q = -5

Simplifying
q = -5
Subproblem 2
Set the factor '(4 + q)' equal to zero and attempt to solve:

Simplifying
4 + q = 0

Solving
4 + q = 0

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

Add '-4' to each side of the equation.
4 + -4 + q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + q = 0 + -4
q = 0 + -4

Combine like terms: 0 + -4 = -4
q = -4

Simplifying
q = -4
Solution
q = {-5, -4}