(q+6)(q-5)=0

Solution for (q+6)(q-5)=0 equation:

Simplifying
(q + 6)(q + -5) = 0

Reorder the terms:
(6 + q)(q + -5) = 0

Reorder the terms:
(6 + q)(-5 + q) = 0

Multiply (6 + q) * (-5 + q)
(6(-5 + q) + q(-5 + q)) = 0
((-5 * 6 + q * 6) + q(-5 + q)) = 0
((-30 + 6q) + q(-5 + q)) = 0
(-30 + 6q + (-5 * q + q * q)) = 0
(-30 + 6q + (-5q + q2)) = 0

Combine like terms: 6q + -5q = 1q
(-30 + 1q + q2) = 0

Solving
-30 + 1q + q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-6 + -1q)(5 + -1q) = 0

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

Simplifying
-6 + -1q = 0

Solving
-6 + -1q = 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 + -1q = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1q = 0 + 6
-1q = 0 + 6

Combine like terms: 0 + 6 = 6
-1q = 6

Divide each side by '-1'.
q = -6

Simplifying
q = -6
Subproblem 2
Set the factor '(5 + -1q)' equal to zero and attempt to solve:

Simplifying
5 + -1q = 0

Solving
5 + -1q = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1q = 0 + -5
-1q = 0 + -5

Combine like terms: 0 + -5 = -5
-1q = -5

Divide each side by '-1'.
q = 5

Simplifying
q = 5
Solution
q = {-6, 5}