(q+2)(3q+5)=

Solution for (q+2)(3q+5)= equation:

Simplifying
(q + 2)(3q + 5) = 0

Reorder the terms:
(2 + q)(3q + 5) = 0

Reorder the terms:
(2 + q)(5 + 3q) = 0

Multiply (2 + q) * (5 + 3q)
(2(5 + 3q) + q(5 + 3q)) = 0
((5 * 2 + 3q * 2) + q(5 + 3q)) = 0
((10 + 6q) + q(5 + 3q)) = 0
(10 + 6q + (5 * q + 3q * q)) = 0
(10 + 6q + (5q + 3q2)) = 0

Combine like terms: 6q + 5q = 11q
(10 + 11q + 3q2) = 0

Solving
10 + 11q + 3q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(2 + q)(5 + 3q) = 0

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 '(5 + 3q)' equal to zero and attempt to solve:

Simplifying
5 + 3q = 0

Solving
5 + 3q = 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 + 3q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3q = 0 + -5
3q = 0 + -5

Combine like terms: 0 + -5 = -5
3q = -5

Divide each side by '3'.
q = -1.666666667

Simplifying
q = -1.666666667
Solution
q = {-2, -1.666666667}