(q+2)(3q-1)=0

Solution for (q+2)(3q-1)=0 equation:

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

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

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

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

Combine like terms: 6q + -1q = 5q
(-2 + 5q + 3q2) = 0

Solving
-2 + 5q + 3q2 = 0

Solving for variable 'q'.

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

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

Simplifying
-2 + -1q = 0

Solving
-2 + -1q = 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 + -1q = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1q = 0 + 2
-1q = 0 + 2

Combine like terms: 0 + 2 = 2
-1q = 2

Divide each side by '-1'.
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}