(q-12)(6q+1)=0

Solution for (q-12)(6q+1)=0 equation:

Simplifying
(q + -12)(6q + 1) = 0

Reorder the terms:
(-12 + q)(6q + 1) = 0

Reorder the terms:
(-12 + q)(1 + 6q) = 0

Multiply (-12 + q) * (1 + 6q)
(-12(1 + 6q) + q(1 + 6q)) = 0
((1 * -12 + 6q * -12) + q(1 + 6q)) = 0
((-12 + -72q) + q(1 + 6q)) = 0
(-12 + -72q + (1 * q + 6q * q)) = 0
(-12 + -72q + (1q + 6q2)) = 0

Combine like terms: -72q + 1q = -71q
(-12 + -71q + 6q2) = 0

Solving
-12 + -71q + 6q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-1 + -6q)(12 + -1q) = 0

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

Simplifying
-1 + -6q = 0

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

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

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

Divide each side by '-6'.
q = -0.1666666667

Simplifying
q = -0.1666666667
Subproblem 2
Set the factor '(12 + -1q)' equal to zero and attempt to solve:

Simplifying
12 + -1q = 0

Solving
12 + -1q = 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 + -1q = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1q = 0 + -12
-1q = 0 + -12

Combine like terms: 0 + -12 = -12
-1q = -12

Divide each side by '-1'.
q = 12

Simplifying
q = 12
Solution
q = {-0.1666666667, 12}