3q^2+8q+4=0

Solution for 3q^2+8q+4=0 equation:

Simplifying
3q2 + 8q + 4 = 0

Reorder the terms:
4 + 8q + 3q2 = 0

Solving
4 + 8q + 3q2 = 0

Solving for variable 'q'.

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

Simplifying
2 + 3q = 0

Solving
2 + 3q = 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 + 3q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3q = 0 + -2
3q = 0 + -2

Combine like terms: 0 + -2 = -2
3q = -2

Divide each side by '3'.
q = -0.6666666667

Simplifying
q = -0.6666666667
Solution
q = {-2, -0.6666666667}