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

Solution for (4q+3)(q+2)=0 equation:

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

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

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

Multiply (3 + 4q) * (2 + q)
(3(2 + q) + 4q * (2 + q)) = 0
((2 * 3 + q * 3) + 4q * (2 + q)) = 0
((6 + 3q) + 4q * (2 + q)) = 0
(6 + 3q + (2 * 4q + q * 4q)) = 0
(6 + 3q + (8q + 4q2)) = 0

Combine like terms: 3q + 8q = 11q
(6 + 11q + 4q2) = 0

Solving
6 + 11q + 4q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(2 + q)(3 + 4q) = 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 '(3 + 4q)' equal to zero and attempt to solve:

Simplifying
3 + 4q = 0

Solving
3 + 4q = 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 + 4q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4q = 0 + -3
4q = 0 + -3

Combine like terms: 0 + -3 = -3
4q = -3

Divide each side by '4'.
q = -0.75

Simplifying
q = -0.75
Solution
q = {-2, -0.75}