(12+q)(2-q)=0

Solution for (12+q)(2-q)=0 equation:

Simplifying
(12 + q)(2 + -1q) = 0

Multiply (12 + q) * (2 + -1q)
(12(2 + -1q) + q(2 + -1q)) = 0
((2 * 12 + -1q * 12) + q(2 + -1q)) = 0
((24 + -12q) + q(2 + -1q)) = 0
(24 + -12q + (2 * q + -1q * q)) = 0
(24 + -12q + (2q + -1q2)) = 0

Combine like terms: -12q + 2q = -10q
(24 + -10q + -1q2) = 0

Solving
24 + -10q + -1q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(2 + -1q)(12 + q) = 0

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

Simplifying
2 + -1q = 0

Solving
2 + -1q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1q = 0 + -2
-1q = 0 + -2

Combine like terms: 0 + -2 = -2
-1q = -2

Divide each side by '-1'.
q = 2

Simplifying
q = 2
Subproblem 2
Set the factor '(12 + q)' equal to zero and attempt to solve:

Simplifying
12 + q = 0

Solving
12 + q = 0

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

Add '-12' to each side of the equation.
12 + -12 + q = 0 + -12

Combine like terms: 12 + -12 = 0
0 + q = 0 + -12
q = 0 + -12

Combine like terms: 0 + -12 = -12
q = -12

Simplifying
q = -12
Solution
q = {2, -12}