6q^2+44q+48=0

Solution for 6q^2+44q+48=0 equation:

Simplifying
6q2 + 44q + 48 = 0

Reorder the terms:
48 + 44q + 6q2 = 0

Solving
48 + 44q + 6q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 22q + 3q2) = 0

Factor a trinomial.
2((6 + q)(4 + 3q)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + q)' equal to zero and attempt to solve:

Simplifying
6 + q = 0

Solving
6 + q = 0

Move all terms containing q to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + q = 0 + -6

Combine like terms: 6 + -6 = 0
0 + q = 0 + -6
q = 0 + -6

Combine like terms: 0 + -6 = -6
q = -6

Simplifying
q = -6
Subproblem 2
Set the factor '(4 + 3q)' equal to zero and attempt to solve:

Simplifying
4 + 3q = 0

Solving
4 + 3q = 0

Move all terms containing q to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + 3q = 0 + -4

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

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

Divide each side by '3'.
q = -1.333333333

Simplifying
q = -1.333333333
Solution
q = {-6, -1.333333333}