(6q+7)(q+6)=0

Solution for (6q+7)(q+6)=0 equation:

Simplifying
(6q + 7)(q + 6) = 0

Reorder the terms:
(7 + 6q)(q + 6) = 0

Reorder the terms:
(7 + 6q)(6 + q) = 0

Multiply (7 + 6q) * (6 + q)
(7(6 + q) + 6q * (6 + q)) = 0
((6 * 7 + q * 7) + 6q * (6 + q)) = 0
((42 + 7q) + 6q * (6 + q)) = 0
(42 + 7q + (6 * 6q + q * 6q)) = 0
(42 + 7q + (36q + 6q2)) = 0

Combine like terms: 7q + 36q = 43q
(42 + 43q + 6q2) = 0

Solving
42 + 43q + 6q2 = 0

Solving for variable 'q'.

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

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 '(7 + 6q)' equal to zero and attempt to solve:

Simplifying
7 + 6q = 0

Solving
7 + 6q = 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 + 6q = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6q = 0 + -7
6q = 0 + -7

Combine like terms: 0 + -7 = -7
6q = -7

Divide each side by '6'.
q = -1.166666667

Simplifying
q = -1.166666667
Solution
q = {-6, -1.166666667}