(10q+9)(q+6)=0

Solution for (10q+9)(q+6)=0 equation:

Simplifying
(10q + 9)(q + 6) = 0

Reorder the terms:
(9 + 10q)(q + 6) = 0

Reorder the terms:
(9 + 10q)(6 + q) = 0

Multiply (9 + 10q) * (6 + q)
(9(6 + q) + 10q * (6 + q)) = 0
((6 * 9 + q * 9) + 10q * (6 + q)) = 0
((54 + 9q) + 10q * (6 + q)) = 0
(54 + 9q + (6 * 10q + q * 10q)) = 0
(54 + 9q + (60q + 10q2)) = 0

Combine like terms: 9q + 60q = 69q
(54 + 69q + 10q2) = 0

Solving
54 + 69q + 10q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(6 + q)(9 + 10q) = 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 '(9 + 10q)' equal to zero and attempt to solve:

Simplifying
9 + 10q = 0

Solving
9 + 10q = 0

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

Add '-9' to each side of the equation.
9 + -9 + 10q = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 10q = 0 + -9
10q = 0 + -9

Combine like terms: 0 + -9 = -9
10q = -9

Divide each side by '10'.
q = -0.9

Simplifying
q = -0.9
Solution
q = {-6, -0.9}