6q^2+48q+42=0

Solution for 6q^2+48q+42=0 equation:

Simplifying
6q2 + 48q + 42 = 0

Reorder the terms:
42 + 48q + 6q2 = 0

Solving
42 + 48q + 6q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + 8q + q2) = 0

Factor a trinomial.
6((7 + q)(1 + q)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(7 + q)' equal to zero and attempt to solve:

Simplifying
7 + q = 0

Solving
7 + q = 0

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

Add '-7' to each side of the equation.
7 + -7 + q = 0 + -7

Combine like terms: 7 + -7 = 0
0 + q = 0 + -7
q = 0 + -7

Combine like terms: 0 + -7 = -7
q = -7

Simplifying
q = -7
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 = {-7, -1}