(2q+4)(3q+1)=

Solution for (2q+4)(3q+1)= equation:

Simplifying
(2q + 4)(3q + 1) = 0

Reorder the terms:
(4 + 2q)(3q + 1) = 0

Reorder the terms:
(4 + 2q)(1 + 3q) = 0

Multiply (4 + 2q) * (1 + 3q)
(4(1 + 3q) + 2q * (1 + 3q)) = 0
((1 * 4 + 3q * 4) + 2q * (1 + 3q)) = 0
((4 + 12q) + 2q * (1 + 3q)) = 0
(4 + 12q + (1 * 2q + 3q * 2q)) = 0
(4 + 12q + (2q + 6q2)) = 0

Combine like terms: 12q + 2q = 14q
(4 + 14q + 6q2) = 0

Solving
4 + 14q + 6q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 7q + 3q2) = 0

Factor a trinomial.
2((2 + q)(1 + 3q)) = 0

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

Simplifying
1 + 3q = 0

Solving
1 + 3q = 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 + 3q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3q = 0 + -1
3q = 0 + -1

Combine like terms: 0 + -1 = -1
3q = -1

Divide each side by '3'.
q = -0.3333333333

Simplifying
q = -0.3333333333
Solution
q = {-2, -0.3333333333}