(q+4)(3q+9)=0

Solution for (q+4)(3q+9)=0 equation:

Simplifying
(q + 4)(3q + 9) = 0

Reorder the terms:
(4 + q)(3q + 9) = 0

Reorder the terms:
(4 + q)(9 + 3q) = 0

Multiply (4 + q) * (9 + 3q)
(4(9 + 3q) + q(9 + 3q)) = 0
((9 * 4 + 3q * 4) + q(9 + 3q)) = 0
((36 + 12q) + q(9 + 3q)) = 0
(36 + 12q + (9 * q + 3q * q)) = 0
(36 + 12q + (9q + 3q2)) = 0

Combine like terms: 12q + 9q = 21q
(36 + 21q + 3q2) = 0

Solving
36 + 21q + 3q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 7q + q2) = 0

Factor a trinomial.
3((4 + q)(3 + q)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + q)' equal to zero and attempt to solve:

Simplifying
3 + q = 0

Solving
3 + q = 0

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

Add '-3' to each side of the equation.
3 + -3 + q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + q = 0 + -3
q = 0 + -3

Combine like terms: 0 + -3 = -3
q = -3

Simplifying
q = -3
Solution
q = {-4, -3}