3q^2+51q+48=0

Solution for 3q^2+51q+48=0 equation:

Simplifying
3q2 + 51q + 48 = 0

Reorder the terms:
48 + 51q + 3q2 = 0

Solving
48 + 51q + 3q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + 17q + q2) = 0

Factor a trinomial.
3((16 + q)(1 + q)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(16 + q)' equal to zero and attempt to solve:

Simplifying
16 + q = 0

Solving
16 + q = 0

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

Add '-16' to each side of the equation.
16 + -16 + q = 0 + -16

Combine like terms: 16 + -16 = 0
0 + q = 0 + -16
q = 0 + -16

Combine like terms: 0 + -16 = -16
q = -16

Simplifying
q = -16
Subproblem 2
Set the factor '(1 + q)' equal to zero and attempt to solve:

Simplifying
1 + q = 0

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

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

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

Simplifying
q = -1
Solution
q = {-16, -1}